At that time the rocket has reached an altitude of 500 m

Question

A rocket is launched vertically. At time t = 0, the rocket's engine shuts down. At that time, the rocket has reached an altitude of 500 m and is rising at a velocity of 125 m/s. Gravity then takes over. The height of the rocket as a function of time is

h(t) = -9.8/2(t²) + 125t + 500 for t>0

(a) Create a function called height that accepts time as an input and returns the height of the rocket. Use your function in your solutions toparts b and c.

(b) Plot height versus time for times from 0 to 30 seconds. Use an increment of 0.5 second in your time vector.

(c) Find the time when the rocket starts to fall back to the ground. (The max function will be helpful in this exercise.)