The upward acceleration is 12.0 m/s2 and it has 10 seconds worth of fuel.
Two rockets are shot from the ground. Each has a different upward acceleration, and a different amount of fuel. After the fuel runs out, each rocket falls with an acceleration of -9.8 m/s2. For each rocket,
a. Write down and solve differential equations describing the velocity and position of the rocket while it still has fuel.
b. Find the velocity and height of the rocket when it runs out of fuel.
c. Write down and solve differential equations describing the velocity and position of the rocket after it has run out of fuel. What is the initial condition for each?
d. Find the maximum height reached by the rocket. Does it rise more with or without fuel. Why?
e. Find the velocity when it hits the ground.