 Yes sir. That's beautiful to hear and here's your mentee code 950468 could you write the formula for 1,000,000. Okay 950468 just so 950468 good yeah good yeah 11 questions okay so you guys want me to write down the formula right so yes this is a mixed batch of vectors 950468 so we will be discussing about multiple operations associated with vectors we will be discussing about questions associated with motions we will be discussing about something about projectile okay yeah so that is why I don't want to state the formula tomorrow is your come on that doesn't sound beautiful if you guys are asking for the formula at this evening okay so no no video yeah are we ready are we ready how many of us are here 54 beautiful 54 people good 53 so yes it's 802 now I am ready okay 55 people and here we go to the question number one two forces A 2 Newton and B 3 Newton are acting along the lines x equal to 0 and y equal to 0 respectively then the resultant of the force would be 1, 2, 1, 1, 3, 2, 2, 1 so there's a slight hint okay so if you'll just try to match the question and the options you will get it that's it if you just try to match the questions and the options you will get it right relax good 40 seconds people have responded that's beautiful that's beautiful that's before people already responded good 40 people got it right as I said just try to match with the let's stop it mate what happened why no spam please no spam okay yes question number one okay no video no video good thank you no two forces A 2 Newton and B 3 Newton act along the line x equal to 0 which line is x equal to 0 this is y equal to 0 this is x equal to 0 so along the y axis it is 2 along the x axis it is 3 so it will be written as 3 i plus 2 j g i got it or not got it or not got it or not yeah exactly see what happens exactly so even I was confused it should be 2 i plus 3 j relax on the y axis what is the value of x what do you mean sir on throughout the y axis what is the value of x throughout the y axis what is the value of x what is this point throughout the y axis the value of x is 0 right so the y axis is also called x equal to 0 throughout the x axis the value of y is 0 so x axis is also called y equal to 0 so instead of directly measuring x axis with y axis with x axis good so in that case what happened 2 new terms is toward x equal to 0 means here 3 new term is toward y equal to 0 means here so this is 3 i and this is 2 j got it very good very good very good good let's look at the leader board 40 people getting it right here we go nishant has a doubt okay nishant we'll come back to you post the leader board mahika was the fastest one to reward good yes nishant that's beautiful but even if you consider that the options are not supporting them right got it nishant nishant got very beautiful very good oh many is on bright mode okay i'm sorry i'm sorry i'm sorry i have created it in dark one second it won't take more than a second okay all good here we go to the next question a is equals to this and b is equals to this are two vectors then the angle between them will be then the angle between them will be then the angle between them will be then the angle between them will be good good good good good good good in order to calculate angle you can take help of a dot product. Yes, there are some special cases also where by just some mere simple operations you can detect only if the two vectors are parallel or perpendicular. If not, then you have the comprehensive formula to be applied of dot product. Yep. So 35 people have answered it. Good. And 20 seconds are remaining. Sir, send help please, send help please, send help please, send help please. Manisha, I have signed the help. Have you received it? Kindly acknowledge. Okay, Nafal, Anush, Bitap have learned dot and cross both. Why? Coincidentally, the bizarreness is I only teach you, no problem. Good, 23, 23, 7. Relax. Relax. Relax. Relax. Relax. Relax. Relax. Relax. Relax. Relax. Relax. Method number one. A1 upon A2 equal to B1 upon B2 equal to C1 upon C2. Is it there? 2 upon minus 6 is 1 by minus 3. Minus 3 upon 9 is 1 upon minus 3. K upon minus 3 is 1 upon minus 3. Yes or no, yes or no, yes or no. Good. Very good. So, yeah, they are parallel. But if this would have been a positive proportion, then 0 degree. As it is a negative proportion, then 180 degree. Gi, got it or not, got it or not, got it or not, got it. Good. Very good. Very good. That kind of thing. Repeat? So, could you like explain it once again? Yep. If you wanted to see, proportions, okay, gives you a parallel sense, okay, the sense of parallel. But as this is a negative proportion, they will not be parallel, they will be anti-parallel and the angle between anti-parallel vectors is 180 degree. Suppose you don't remember this and you want to comprehensively go for the dot product. So, your answer will be like cos theta is equal to dot product of the two vectors divided by their individual magnitudes, okay, magnitude of A and magnitude of B. So? Yes, sir. Clear? You want me to operate that? Sir, I got it. Okay, good. Thank you very much. Relax. Anush? Yeah, okay, okay, Vignesh, okay, okay, relax. So, dot product of A to B is I multiplied with I minus 12, J multiplied with J minus 27, K multiplied with K minus 3 divided by magnitude of A, magnitude of B, magnitude of A is 9, 4, 13 plus 1, 14. Magnitude of B is, clear? 36 plus 81 plus 9, clear? Excuse me. 1, 26. Yes, dear? Yes, sir. That's what I initially stated, but sir, that's what I initially stated, but our friends are like, sir, can you like do it by comprehensive method? We don't want to remember a property, okay, clear? Good. Now dear, I am going to open the link, okay, the YouTube link, okay. If I am finding something terribly irrelevant, okay, sure. Sir, it's how to make chutney. Sir, it's not how to make chutney. Next question, and the board will get the scoreboard. Vihana was the fastest one to respond. Leaderboard, and here we go to the third question. Two constant forces, one is A in Newton and another is B in Newton, act on a body and displace it from position R1 to the position R2. What is the work done? If you remember, in our last conversations, we have had the discussion of how is work done calculated. And the answer is, what is done is calculated by the dot product of force and displacement by the dot product of force and displacement. By the dot product of force and displacement, by the dot product of force and displacement. Sir, what is the Java? Repeat that. Notize none of the above, none of the above. Okay, Monisha, no problem. Aditya, that's not the proper place to respond, right? 22 people got it, right? Let's look at the scene. Yes, the primary thing which is required as a prerequisite for this question is that we should know that work is force dot displacement, right? What is force? The total force is being supplied in two ways, clear? So, the total force is 3, 2, minus 2, clear? The total displacement is moving from R1 to R2 means final minus initial, 7 minus 1, 6, 10 minus 2, 8, 5 minus minus 2, 7, clear? So, the total variation, the dot product is 6, 3, 18, 8, 2, 16, minus 14. Okay, this will deliver you 4 and this will deliver you 20. Got it? Now, this time in white color, okay? Total force is being supplied from two sources. So, what is total force? Total force will be the sum of A and B, which is 1, 2, 3, I, 3, 1, minus 2, 3, minus 1, 2, minus 3, plus 1, minus 2, okay? Got it? Step number 1, calculation of net force. No, no, no, no, no, no, relax. Relax, relax, relax, Manisha. Two constant forces A and B act on a body. So, when two forces act on a body, we have to calculate the total force acting on the body and that will be calculated by A plus B, okay? Shop, good. Let's add I to I, 3 I, minus J to plus 3 J, plus 2 J, plus K to minus 3 K, minus 2 K. Got it? Manisha and other dear friends. So, there wasn't enough time. Relax, there was enough, 90 seconds. So, there was enough time. 90 seconds for the 90 seconds is fairly enough, okay? No problem, no problem, it's okay, good. Then comes, this is what? Total force, yeah? Then comes total displacement. Now, the case where displacement is different. You are going from R1 to R2. Final minus initial will give you some answer. What is final minus initial? So, the displacement is final minus initial 6 I, final minus initial 8 J, final minus initial 5 minus minus 2 is 7 K. Got it? Okay, good, good. Talk formula. Repeat? Talk formula. Talk is R cross F, R cross F is top, okay? You can note these down as cheat codes for tomorrow. So, what is R in that? Position vector. Oh, okay, yes sir. Yeah, good. So now, we have two vectors and we have to perform the dot product between them. What is the dot product? I to I 18, J to J 16, K to K minus 14, 12, 20. Got it? Got it? Anisha, good, very, very, very good. I had to reload my thing when you were saying the talk formula. Could you just write it again? Okay, there will be two things which are expected to be asked, okay? Work done. Work done is force multiplied by displacement, but a dot product. Torque is position vector cross multiplied with force, okay? Yeah, going on to the leaderboard. Good. Next question. For any two vectors a and b, if a cross b is equal to 0, the magnitude of c equal to a plus b is equal to square root of a square plus b square, just a plus b, square root of a square plus b square plus a b whole by root 2 or a square plus b square plus root 2 a b, okay? The formula is derived or being taken up from square root of a square plus b square plus 2 a b cos theta. Cross product formula, cross product, you make a matrix i, j, k and all that, okay? Yeah, this is all there. I tried using my head, but it's all machine good. Drove, very good. Matrix multiplication would have been required, provided it would have been a cross product in the solution. The solution is an addition. So you have to go for additional requirement. What are the requirements in order to calculate the addition? 21, 12, 14, 15. Relax. Very easy. Relax. Look at it. For any two vectors a and b, if a cross b is 0, what do we mean by a cross b is equal to 0? That's sin theta equal to 0 or theta equal to 0. Am I right? So what is the formula of cross product like that magnitude of a plus magnitude of b? A cross b is equals to magnitude of a magnitude of b sin theta multiplied with a unit vector n. The only value 0 making, okay, thingy is sin theta. Okay, okay, okay, okay. Good. Sin 0 is 0. Got it. Theta is 0. Now when theta is 0, then square root a square plus b square plus 2 a b cos 0 will look like this, which is a plus b whole square a plus b. Got it? So could you just write that cross product equation that you have written again, sir? Okay, no problem. Dot product is magnitude of a magnitude of b cos theta. Cross product is magnitude of a, magnitude of b sin theta multiplied with a unit vector mutually perpendicular to both a and b. No problem. Relax. Good. Good, good, good. Good. Just refresh one time, Aditya. That might help. Good. Let's look at the leadboard. Could you repeat the last part? Okay, Shivam, I'll come back and repeat it. Okay, look here. Are you okay till we get theta equal to 0, Shivam? Yes, sir. Good. Now when theta is equal to 0 and we are calculating the addition, we know that the magnitude of addition is given by a square plus b square plus 2 a b cos theta. What is the value of cos 0? 1. This looks like a square plus b square plus 2 a b, which is a plus b whole square will nullify the square root answer b a plus b. Got it? Yes, sir. Very good. So basically the 2 a b cos theta will become 0, right? But that would have become 0 provided theta would have been 90. That will remain. Then only causing the a square plus b square plus 2 a b to become a plus b whole square. And hence nullify the square root answer. Got it? Oh, I understood, sir. Sir, in cross product, in the bracket, do we add or subtract beta? In cross product, we don't have an addition or subtraction involved. Okay, got it. In the matrix method, yes. By default, there has to be subtraction. Like this is this, this is this. Suppose this is a, b, c, d, you will be writing a, b minus c, d. So, yes, the leaderboard, the leaderboard, the leaderboard. Shiran is leading the scenario. Good. Here we go to the next one. If a body covers one fourth distance in one, at a speed one. Okay. Next one, fourth at a speed two. The next one, fourth at a speed three. And the last one, fourth at a speed four. I'm dead. I'm gone. Saranda. Good. Confusing, right? Though why, why? It's not scary. Nothing about me is scary. Only thing coming to my mind is one fourth, one fourth. 20 people got it right. Beautiful. Beautiful. So, wasn't it 4.8? Let's see. It might be wrong also. No, no problem. Relax. So, see. If you know that when it is about two, the answer is two v1, v2 upon v1 plus v2. Yes or no? Yeah. So, when they are three, when they are three, when they are three, when they are three, the answer is three v1, v2, v3 upon v1, v2, v2, v3, v3, v1. Similarly, when they are four, we have four v1, v2, v3, v4 divided by v1, v2, v3. v2, v3, v4. v3, v4, v1, v4, v1, v2. Got it? Pat it. Pat it. Pat it. You can also prove it the same way. Sir, I just calculated it. I didn't use the formula. Exactly. Now, you can go like, sir, why are we investing our time in this? We can be like, total distance covered is boom. Total distance covered is sum of 1 by 4, 1 by 4, 1 by 4, 1 by 4, 1. Yes or no? Speed is equals to distance upon time. So, time is equals to distance upon speed. In the first part, the time taken is 1 by 4. In the second part, time taken is 1 by 8. In the third part, time taken is 1 by 12. In the fourth part, time taken 1 by 16. Yes or no? Yes or no? Yes or no? Yes or no? Good. Speed is equals to distance upon time. So, time is equals to distance upon speed. In the first part, distance is 1 by 4, speed is 1. In the second part, distance is 1 by 4, speed is 2. In the third part, distance is 1 by 4, speed is 3. In the fourth part, distance is 1 by 4, speed is 4. Got it? Got it. With all the ways I have given. Okay. Can you please explain once again? Okay, good. For V1, V2, V3, V4 divided by V1, V2, V3. Sir, can you please change the color? V2, V2. Okay, okay, okay. V1, V2, V3, V3. V1, V2, V3 plus V2, V3, V4. Clear? Clear? Clear? V3, V4, V1. Got it? You write it in the formula form like instead of writing it in the numbers form. But I did wrote it in the formula form. For V1, V2, V3, V4, V1, V2, V3, V2, V3, V4. V3, V4, V1. V4, V1, V2. Clear? Numerator looks like beautiful. 4 into 2, 10 to 3, 10 to 4. Clear? Now, why? Barat, V4, Pachas. This is 4. Sir, in the denominator, okay. Now, we'll be like, okay, all the denominators are at least 25. So, divided by 2, numerator 2, 4, 4 to the 16, 3 is a 48. Yes, so, 48 by 25. Got it? So, it cannot be this complicated? This one is not complicated at all. Or this one, like the other one. Complicated till now, which one was complicated? No, like, will it be on the same level? Relax. This is a warm-up session. It is not required. That's absolutely not required. Sriram is still leading the synapse. Here we go to the next question. But he is running a straight road with a speed of 10 meter per second. A police man chases him on a motorcycle, moving at a speed of 20 meter per second. The instantaneous separation of the jeep from the motorcycle is 50. How long will it take for the police to catch the thief? I have my answer with me. You should know subtraction and you should know division, right? Please put your mics over mute from somewhere. Household poi system. Please mute. Yeah. Thank you. Thank you, Adityanand. Good. What if people got it right? That's beautiful. You didn't even need to solve so too easy. Yeah. Yes, you don't need to solve. Oh, no, not required. Please, please. The police man, the thief. The thief is going at a speed of 10. The police man is going at a speed of 20. The difference between their speeds, which is their resultant speed is 10. The distance between them is 50. So it will take five seconds to catch the thief. Gee, I got it. Good. So can you please explain? Okay, I'll explain that. No problem. For very obvious reason, for a chase, they will have to run in the same direction, right? When two objects run in the same direction, their velocities are subtractive. Subtracting their resultant outcome will be coming as 10. Okay. The distance between them is 50. So 10, 5, 5 seconds. Gee, I got it. No, please. Mommy, I have muted my mic. Relax. Yeah, mute. Rishabh, could you mute? I'll try if I can mute everyone. Have I muted everyone? Yes, I guess. Have I muted myself? No. Sir, can you proceed? Yeah. So Arthur missed it. Shriram, good. Pratham, very good. And here we are moving toward the next one. Next question. Thank you, Manisha. That's really like, wow, respect. Beautiful. Wow. This one of length 50 meter and another of length 62.5-metre-cut train are moving in mutually opposite directions along parallel lengths. Meet each other each with 5-metre per second. Woof. If their accelerations are brr and brr, then the time they take to pass each other will be, okay. And the time they take to pass each other, not today, not today. So that's not today. It will be happening tomorrow. Okay, Dhruva, I'll be surely explaining the question, but think about it. Think about it, think about it. Think about it. Two trains. Good. Good. Relax. Relax. Relax. Relax. Relax. Two trains. Sir, isn't it 20 seconds? Let's see. But it might be 20 as well. I might make a mistake in calculations, okay. Two trains, one of length 50 and another of 62.5. So this is 112. 112? Yes. So total displacement is 112.5. No doubt. Are moving in mutually opposite direction, okay, along parallel lengths. Meet each other with speed 5-metre per second. So resultant speed they are meeting with each other is 10-metre per second. Yes or no? Yes or no? Yes or no? As they are moving in opposite direction, right? If their accelerations are drum and drum, as they are moving in opposite direction, even their accelerations will get added. So this is the initial velocity. Their accelerations are 10, 15, 0.25-metre per second square. Yes or no? Yes or no? Yes or no? So can you please repeat? Good. I'll repeat with you. First thing we have to calculate that what is the total displacement to be covered in order to cross each other. That will be the sum of the lengths, okay, part one. Sure. Then with what initial velocity are they meeting each other? So as they are meeting each with 5-metre per second moving in opposite direction, but finally like the actual resultant velocity act, clear? Sure. They will be meeting. Is it 5 plus 5, 10-metre per second? Got it. The total effective acceleration will be the acceleration of one plus the acceleration of other as they are moving in the opposite direction, okay? Sure. So our calculations will go like S is equals to U T plus half A T square. Good. So it's much easier to convert it to a fraction. Yeah, I'll come to that only. Very, very good. Okay. I won't even attempt to solve the equation. Rather, I'll use the substitution. But it's okay. One of our friends is saying that sir converted to by 10. So it will become 1, 1, 2, 5 by 10 is equals to 10 T plus, can you see this? 25 by 200 T square, clear? In order to neutralize it, you will have to multiply by T square, okay? So 200 when you multiply, how did you get U equal to 10 beta? There are two trains each moving with 5-metre, okay? Relax, guys. No mockery when we are clarifying our friends doubt or don't consider them friend. Simple. Got it, Monisha? How I got A equal to 0.25 beta? There are two accelerations, one and two. Both accelerations are in opposite directions. We will get added 0.25, okay? Arushi and anyone else? Arushi is actually doing a favor. There are many friends of ours who by God knows what hesitation are not asking even if they have doubt. So Arushi is actually helping them out. Good Arushi. No, so I haven't got the times yet, okay? We have still reached to the equations, okay? That will not be deserving your love from Monday. Okay, ready? Sir, I think Nitya wanted you to explain again. Okay. From where with it? S, U, A is clear. Yes or no? No, let's not discuss about this part. If S, U, A is clear, then fairly enough. Clear. Nitya, now when S, U, A is clear, when S, U, A is clear, we have S sorry, long color is equal to U, T plus half A, T square. Got it? Got it? Got it? One of our friends suggested that this is a bit more different. I have to buy 8. Someone said something in between. I missed it out. Please repeat. Sir, can you reflect just do the calculations a little further? Yeah, I'll do. I'll multiply the whole equation by 8. Why will I do that? Because I want to make this as 1, okay? Clear? Or I want to take the LCM, okay? Whichever way? Clear, clear, clear, clear, clear. 8 times this is equals to 8, 5, 4, T, 16, 4, 10. 10. Yes or no? Yes or no? Yes or no? Yes. Is equals to 80 T plus T square. This is not 2. This is a 9. Yep, got it? Got it? Okay, good. Let's do it by conventional method, okay? Take the LCM. So you will be like 1, 1, 2, 5 by 10. Equal to 10 T plus 25 by 100. That is 200 T square. Got it? Clear? Please take the LCM as 200. It will become easier for you, okay? You will get an equation. No need to solve that equation. That's my suggestion. Because options are very much in your favor, okay? If you want to solve, there is a Sri Dharacharya rule. That T equal to minus B plus minus under root B square minus 4 AC whole by 2A. Got it? No, that's C. So why is B in this? B, okay? So this is being taken up from a quadratic equation which looks like this, okay? So B is the coefficient of T. A is the coefficient of T square. C is the constant part. Tony, hello? Tony, you will get the update from Hirrahit. He has already sent it, I guess, okay? So could you please repeat the last two steps? One second, one by one. The first one, please. Sir, could you please? Sir, repeat the last two steps. Okay? You got this, Vachir? You got, you reached through this equation? Yes, sir. Good. For solving it, the easier method is to multiply it by 8. When you multiply it by 8, you get 900 is equals to 80T plus 2A square. So why do we need to multiply by 8? To in order to simplify that equation, Vachir? Yeah. If you want, you can proceed like that also, no problem at all. Clear? Good. Just looking at it, it will be smiling at you, yeah? This is 800 and this is 100, which will be delivered by a single option straight. Got it? Yes. Sir, it's 853 and we have four questions left. No problem, Vachir. We can do that. No problem. Do we have any true or false? Kind of. Relax. Good. Sir, I think one of those questions would be the opinion and how do you like it? No, no, not at all. Leave the board. Krishna, Paghi, why you bully me? Who is bullying you? Who is this? Charo. Good. Here we go to the next one. No problem. Three marbles are dropped from the top of a tower one after the other with an interval of one second. Okay. The distance between the first and the third after four seconds will be. Relax, read and respond. Yes, you like that chair. Sorry, you won't hear that sound from Monday. Good, very good, very good, very good. Read it, think and respond. Everything when is being dropped is dropped means initial velocity u is 0. By s is equals to ut plus half a t square. You can get an easier response. Misclicked like an idiot. Don't hit there, please. Which Wi-Fi network do you use? I'm using A10 and 2115 people got right. Look here, relax. Let's hurry up a bit. Three marbles are dropped. First, second and third. First one at t equal to 0 in four seconds will cover ut plus half a t square. 8g, yes or no, yes or no, yes or no, yes or no. Why will I even count the second one? Because I am focusing on the third one. Third one for four seconds will only travel for two seconds. Yes or no, s is equals to ut plus half a t square 2g. The difference between them is 8g minus 2g which is 6g 6t. Got it? Anush, what happened here? Very good, very good Anush, relax. Good, good, good, repeat. Ashish, no problem. Nitya, I'll repeat. So, see. At t equal to 0, a stone is dropped at four seconds. After four seconds, what will be the displacement covered? Displacement covered will be ut plus half a t square. Four square is 16 and half is 8g. Got it? Nitya, Arun and any other friend of mine, like don't. At t equal to one second and 10t equal to 2, the third one. So, while the clock counts four seconds, the third stone will only travel for two seconds. Yes or no? Good. What is the displacement covered in two seconds? ut plus half a t square 2g. What is the difference between them? 8g minus 2g that is 6g which is 6t. Got it? Next question and before that, did both. Very good Nitya, very good. Very good Anush, very good Nitya, very good, very good. Very good. Here we go to the next one. Two bodies are thrown simultaneously from a tower with same initial velocity 20m per second, one vertically upward, the other vertically down. The distance between the two bodies after one second is? That's an easy one. One is upward, okay. One is downward, okay. After one second, displacement covered by one body is in one second, displacement covered by another body in one second, as both are covering displacements in opposite directions, just add them, you should get the answer. Dhruv is asking, what's your mother tongue Hindi? Dhruv, good Gargi, very good. Very good Tanya, very good. Very good Siddharth, why Gargi? Nitya, that's okay, okay, okay, no problem. Okay, okay, so isn't it 40m? Like how will you say isn't it 40m just by 7, 8, 9, 40? Let's see. So it's 8. Let's see, let's see, relax. Okay, this is the neutral point. From here one body is thrown up with 20m per second, one body is thrown down with 20m per second. The displacement covered down is ut plus half a t square, which is 25. The displacement covered up will be ut plus half minus, minus, minus, minus, minus, 10 t square. This is 15, 15 plus 25, answer should be 40. Oops, I guess there's a misprint, I guess there's a misprint here. Okay, so make a right, yeah. Excuse me, so I have a doubt. Yeah, the answer is A or B. Yeah, yeah, yeah. When you have to find the distance between the two, you have to add the, okay, sorry. You need D right? Make it A right, because that's like the closest. Yeah, yeah, yeah, exactly, no. There is a misprint only, I can understand that. Sir, please get it deleted, we all got that. No, no, no, sir, A is right because it's the closest. Yes, sir, because it's the subtraction of the two. Sir, the best option will be to delete this. Yes, sir, please get it deleted. The best option will be to delete this question. Sir, can you just read all the questions all of us can mark it? No, that will be a bias. So no problem, we got the solution, which is the important part over here. Yeah, we are moving on to the next question. This question I have deleted. Okay, so that it won't be influencing your leading roles. Yeah, here we go to the next one. It's not a leader. No, that's what that's what last question. Okay, so why in the world have you been wondering it in 30 seconds? Because I wanted to see whether it will come as everyone has responded. I hope everyone has responded. Yeah, sir, is there a trap in this? No, no, no, no. Very plain spray. Everybody has been asked that the past sense of hard has been lost. 54 people got it right. No problem, no problem. I have marked it wrong. What is D? Sir, if that actually happened, the leaderboard would change. Yeah, no, no, no. One second, one second, one second. Okay, why it happened? I guess, one second. I just deleted the question, not the answer mark. Okay, one second. How can this happen? But if D was true, then Kmon would have been much easier. Yes, we are here. Yes, we are here. Sir, can you change the answers for Kmon this time? Because last time in physical... I have seen, I have seen, I have checked the question. No error, no error at all. Okay, there was one error in marking of one of the answers that has been corrected. Okay. Sir, only explanation is correct. Yeah, here we go to the next one. Charani, both A and B, a vector will have, good. Krishna, Krishna, Krishna, go. Here we go to the final question. The height y of the distance and the distance x along the horizontal plane of a projectile on a certain planet are given by y equal to Brom and x equal to Brom, where t is in seconds. The velocity with which the projectile is projected is, okay, got it. I got it. I got it. Sir, are these type of questions going to come in Kmon? I'll explain you this much. You will not be feeling it difficult. Okay. At this vision, you might find it difficult. Okay. But then the next show, you will never find it difficult. Okay. Good. Sir, 12, 5 and tell something, I guess. 12, 5, you got the answer. Square root. Good. Relax. Very good. You guys got it right. Very beautifully. No, I don't think so. It was correct. There was no way we could have obtained this from the data. Why? From the data only? Sir, we need just 12, 5 and then 13. I don't think so. No, no. See, I understand. Understand this. This is the x-axis and y-axis. You know, at the y-axis, the initial velocity is u sin theta. And at the x-axis, the initial velocity is u cos theta. If I want the height in y at any random point, s is equal to u t minus half a t square. Any doubt in this? Can you relate with this? u t. So, which oh, okay, nothing. Half a t square. Got it? But a projectile performs two motions simultaneously. One in the vertical direction and one in the horizontal. The horizontal displacement without presence of any acceleration is given by s is equals to u t only, whereas the vertical displacement because of the presence of acceleration due to gravity is given by u t, sorry, sin minus half a g t square. Got it? From here, you got, okay, u cos theta is 5. U sin theta is 12. Sir, one second. On a certain planet, we don't know what the g is on a certain planet. Dear, that's what is the crack, no? That's why this 5 is given. Clear? That's okay. On certain planet, half acceleration due to gravity should be there. Coincidentally, oh, okay, half g, right or not? It's g for any planet only. For Earth, g is not 10. For Earth, g is 9.8, right? If they'll write for Earth, then there's some s. Okay, good. Sir, I bet no one would have calculated this. Exactly. That's why I told you, when I'll reveal that, okay, how you should look at this question, then it might become easier. Few of you even got while reading the question that, oh, that's the only part you have to put your brain in. That's okay, 12, okay, 5, square root. This is 12, this is 5. So the resultant is the actual launch velocity, which is 13 meters per second. Got it? Good. Thank you very much. The paper check? Oh, my, my. Okay, good, okay. So this was very complicated, sir. Good. Sir, this was. That's why I kept it. This was why I insisted. So will Kamal have questions like these, sir? Yeah, how many questions like these? Why, why I insisted that today I want to keep a centum R was the primary. This is the primary. Sir, if this is going to be there, then I think I need three hours to do only three. Okay. Krishna, see a nine, six, four, three, seven. Very good. Very good. Thank you very much for your time, guys. You were really good. Just don't do that. Okay, so I think it really. Thank you, sir. Bye. Thank you, sir. Thank you, sir. Thank you, sir. Thank you, sir. Not any sentence. Thank you, sir. Bye, sir. That will be sent in kind of 25 minutes, okay. Because it takes more than 20,000 minutes for the recording to get done. Bye, bye, bye, bye, bye. Thank you, sir. Bye, bye, bye, bye, bye.