A rocket launches vertically from ground level while a camera located 500 m away on…
MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A rocket launches vertically from ground level while a camera located 500 m away on level ground pans upward to keep the rocket in view. The angle θ between the ground and the camera’s line of sight increases as the rocket rises. The rocket’s vertical speed remains constant at 50 m/s. Which statement correctly compares the camera’s angular speed dθ/dt when the rocket is 500 m above the ground with dθ/dt when the rocket is 1000 m above the ground?
(a) dθ/dt is greater when the rocket is 1000 m high than when it is 500 m high.
(b) dθ/dt is the same at both altitudes because the rocket’s vertical speed is constant.
(c) dθ/dt is smaller when the rocket is 1000 m high than when it is 500 m high.
(d) The information provided is insufficient to determine how dθ/dt at the two altitudes compare.