 Hello and welcome to the session. In this session we discussed the following question which says, A straight highway leads to the foot of a tar. A man standing at the top of the tar observes a car at an angle of depression of 30 degrees, which is approaching the foot of the tar with a uniform speed. Six seconds later the angle of depression of the car is found to be 60 degrees. Find the time taken by the car to reach the foot of the tar from this point. Let's proceed with the solution now. First of all we take, let this AB be the tar. Let the height of the tar that is AB be equal to y units. In the question we have that a man standing at the top of the tar observes the car which is approaching the foot of the tar with a uniform speed. And six seconds later the angle of depression of the car is changed from 30 degrees to 60 degrees. So we have DNC be the positions of the car such that we have BC equal to x units. Now we assume that the speed of the car be equal to z units per second. As in the question we have that the man standing at the top of the tar observes the car at an angle of depression of 30 degrees. So this angle is of measure 30 degrees since the angle of depression is 30 degrees. Then six seconds later the position of the car is changed from D to C and the angle of depression of the car is 60 degrees. So this angle is 60 degrees and hence this angle would be 60 degrees. We need to find the time taken by the car to reach the foot of the tar from this point. That is from the point C. Let's now consider the right triangle ABC in this 1060 degrees is equal to AB upon BC. Now 1060 degrees is root 3. So root 3 is equal to AB that is Y upon BC which is x. As we get Y is equal to root 3x. Let this be equation 1. Next we consider the right triangle ABD in this 1030 degrees is equal to AB upon BD. The value for 1030 degrees is 1 upon root 3. This is equal to AB that is Y upon BD. Now BD is equal to BC plus CD. Let's find out what is CD. Now CD is the distance traveled by the car at the speed of Z units per second in 6 seconds as given in the question. So CD would be equal to now distance is speed into time that is 6 Z units is CD. Therefore we have 1 upon root 3 is equal to Y upon BC plus CD or BC is x plus CD which is 6 Z. Now for equation 1 we have Y equal to root 3x. So substituting Y equal to root 3x here we get 1 upon root 3 is equal to root 3x upon x plus 6 Z. So now cross multiplying we get 3x is equal to x plus 6 Z which gives us 2x is equal to 6 Z. Now you can say we have x is equal to 6 Z upon 2 that is equal to 3 Z. Now since we need to find the time taken by the car to reach the foot of the tar from the point C. So for this we have got the distance of the car from the point C to the foot of the tar that is x which is equal to 3 Z. That is x is equal to 3 Z units that is we have CD is equal to 3 Z and we know that the speed of the car is equal to Z units per second. Thus the required time would be equal to distance upon speed that is 3 Z upon Z which is equal to 3 seconds. So the final answer is 3 seconds. This completes the session. Hope you understood the solution of this question.