Question

Suppose that you are watching a spaceship take off. You are 100 meters from the launch pad, and you measure the angle made by the rocket and the ground to be increasing at a rate of (d)(theta)/dt = 0.1 radians per second. What is the velocity of the rocket when theta = pi/4?

Answer 1

draw a diagram. You can see that if the rocket is at height y,

tanθ = y/100
so,
sec^2θ dθ/dt = 1/200 dy/dt

Now just plug in your numbers and find dy/dt