The height of a rocket can be calculated during the first five seconds with the equation h1=t3 in which h1 is the height in meters during those five seconds and t is the time in seconds after starting at t=0. After exactly 5 seconds the engine falls apart and the height is given by the equation h2=-5t2 + 125t - 375.
(basically it would look something like this)
The speed of the rocket you can approach with the differential quotient of the height over an interval with the length of 0.001 seconds.
a. What would be the speed of the rocket in m/s after 5 second with a differential quotient over an interval of [5; 5.001]
b. Verify that the height on t=5 is the same in both equations
c. Also find out whether the speeds at the transition of one equation to the other are the same.
d. Calculate after how many seconds the rocket falls to the ground.
e. Explain how you can see in the graph that the speed was the greatest at t=5
