2019 · Q23
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?
Elementary MathematicsTrigonometry
- A75 seconds
- B90 seconds
- C105 seconds
- D135 seconds
Explanation
Equal elevations at t and t+30 are symmetric about the point of minimum elevation (the farthest point), reached at t+15 s. The point of maximum elevation (directly overhead P) comes half a revolution, 90 s, later. Hence x = 15 + 90 = 105 s.