A rocket is propelled vertically upward from a launching pad 150 metres away from an observation station. Let h be the height of the rocket in metres and θ be the angle of elevation of a tracking instrument in the station at time t in seconds, as shown in the diagram below. (a) Using trigonometry, find an equation relating h and θ. (b) Find dh/dθ. (c) If the rate of change of the angle of elevation θ with respect to time is 1.5 radians per second, find the vertical speed of the rocket (the rate of change of height with respect to time) when θ=π/4.

Question

A rocket is propelled vertically upward from a launching pad 150 metres away from an observation station. Let h be the height of the rocket in metres and θ be the angle of elevation of a tracking instrument in the station at time t in seconds, as shown in the diagram below.

(a) Using trigonometry, find an equation relating h and θ.

(b) Find dh/dθ.

(c) If the rate of change of the angle of elevation θ with respect to time is 1.5 radians per second, find the vertical speed of the rocket (the rate of change of height with respect to time) when θ=π/4.