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A plane is going in circles around an airport. The plane takes 3 minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to?

A plane is going in circles around an airport. The plane takes 3 minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to? Correct Answer 105 seconds

Let the plane be at point A at t se conds and at point B after t + 30 seconds Since the motion is uniform, we can say that at time t+15 seconds, the plane is above the point is diametrically opposite to the point P from where the angle is same. Now since the time taken to cover the full circ le is 3 minutes (180 seconds), the time taken by the plane to reach the diametrically opposite point will be 90 seconds. So the time after which the plane reaches the point P will be = t+ 15 + 90 seconds = (t + 105 )seconds    

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