1. Rocket Crash. A rocket launched in the upward direction moves with acceleration a for a time T before its engines tragically shut off. What goes up, must come down.
a. Draw a graphical representation of the rocket's motion from blast off to crash. Be sure to appropriately label important features of that graph.
b. Write a mathematical representation of the rocket's motion, beginning at the instant that the engines shut off.
c. How much time elapses between the engines shutting off and the rocket crashing into the ground? Express your answer in terms of g and the known quantities above.
d. What would the acceleration of the rocket had to have been in order that the time the rocket ship was in the air with its rockets blasting be equal to the time the rocket ship was in the air after its engines shut off?
2. Rocket Splat. Actually, the rocket launchers of the first problem had thought ahead about the possibility of a crash. They prepared a cannon that fires an explosive shell at the instant that the rocket engines cut out. In order that the cannon shell hit the rocket at the peak of its trajectory, at what velocity v0 does the cannon shell have to be fired?