 Hello and welcome to the session. Let us discuss the following question. Question says, Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 meter above the surface of the water and the fly at the end of the string rests on the water 3.6 meter away and 2.4 meter from a point directly under the tip of the rod. Assuming that her string is taught how much string does she have out. If she pulls in the string at the rate of 5 centimeter per second what will be the horizontal distance of the fly from her after 12 seconds. This is the given figure. Now let us start with the solution. We know tip of her fishing rod is 1.8 meter above the surface of the water and the fly at the end of the string rests on water 3.6 meter away from her and 2.4 meter away from point directly under the tip of the rod. Now in first part of the question we have to find out that how much string does she have out. If we consider this triangle we know this side of the triangle is 1.8 meter this side is 2.4 meter and we have to find this side. Now we can apply Pythagoras theorem to this triangle. Let us name this distance as BC this distance as AB and now we have to find AC now we can represent this triangle as this triangle here AB is equal to 2.4 meter and BC is equal to 1.8 meter now we will apply Pythagoras theorem in this triangle. We know my Pythagoras theorem square of hypotenuse is equal to sum of squares of other two sides so we get AC square is equal to AB square plus BC square now substituting corresponding values of AB and BC in this equation we get AC square is equal to square of 2.4 plus square of 1.8 now this implies AC square is equal to 5.76 plus 3.24 we know square of 2.4 is 5.76 and square of 1.8 is 3.24 now this further implies AC square is equal to 9 now taking square root on both the sides we get AC is equal to 3 meters we know AC is the length of the string she have out so length of the string she have out is equal to 3 meter now we know Nazima pulls the string at the rate of 5 centimeter per second and time for which she pulls the string is equal to 12 seconds so we can find out length of the string pulled at the rate of 5 centimeter per second in 12 seconds so we can write length of the string pulled at the rate of 5 centimeter per second in 12 seconds is equal to 5 multiplied by 12 we know this is the speed this is the time and we have to find distance covered now distance covered is equal to speed multiplied by time so here we have multiplied 5 and 12 where 5 is the speed and 12 is the time so we get length of the string pulled is equal to 60 centimeter now this is equal to 0.6 meter we know length of the string she have out is equal to 3 meter and length of the string she has pulled is equal to 0.60 meter now remaining string left out is equal to 3 minus 0.6 so we can write remaining string left out is equal to 3 minus 0.6 meter now this is equal to 2.4 meter now length of the remaining string is equal to 2.4 meter and we know this distance will remain same that is it is 1.8 meter you have to find this distance now now let us assume that P is the new position of the fly after she pulls away the string so Pc is equal to 2.4 meter and Cv is same as earlier that is 1.8 meter now in this triangle we will find out Pb now in right triangle Pbc Pc square is equal to Pb square plus dc square by Pythagoras theorem now here we will substitute corresponding values of Pc and dc so we can write 2.4 square is equal to Pb square plus square of 1.8 we know square of 2.4 is equal to 5.76 5.76 is equal to Pb square plus 3.24 we know square of 1.8 is 3.24 now this implies Pb square is equal to 5.76 minus 3.24 now this further implies Pb square is equal to 2.52 now taking square root on both the sides we get Pb is equal to square root of 2.52 now square root of 2.52 is equal to 1.59 approximately so we get Pb is equal to 1.59 meter we know C is the tip of the rod and P is the new position of the fly so Pb is the horizontal distance between new position of the fly and a point under the tip of the rod we know horizontal distance between Nazima and point under the tip of the rod is 1.2 meter now we can find total horizontal distance between Nazima and new position of the fly it is equal to Pb plus 1.2 meter we know Nazima is sitting 1.2 meter away from point P so we can write horizontal distance of the fly from Nazima after 12 seconds is equal to 1.59 plus 1.2 meters now this is equal to 2.79 meters so this is our required answer this completes the session hope you understood the session take care and have a nice day