A plane is going in circles around an airport The plane takes 3 minutes to complete one round The an...........

Quantitative Aptitude (CDS) Coordinate Geometry

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?

75 seconds

90 seconds

105 seconds

135 seconds

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Explanation:

Let the plane be at point A at t seconds 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 circle 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