Answer to Question #238271 in Classical Mechanics for Danny

Question

Question 2

SpaceX plans to transport humans to Mars, but experienced a few rocket failures while on initial tests. So suppose the rocket to Mars (without people on board - another test flight) liftoffs from earth, from rest, with an acceleration of 52.0 m/s². Unfortunately, after 8.15 s, the rocket experiences a failure and shuts off. It then continues to coast upward (with no appreciable air resistance). What is the maximum height the rocket reaches above the surface?

Answer 1

$l_1=\frac{at^2}2=1727~m,$

$v=at=423.8~\frac ms,$

$l_2=\frac{v^2}{2g}=9154~m,$

$l=l_1+l_2=10881~m.$