max height of object above the surface

Question

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 47.0 m/s². Unfortunately, after 7.75 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?

In my previous attempt at this question I first found the final velocity before shut down, then substiuted it into the acceleration equation to find the displacement, however it seems that however i did it was incorrect.

Answer 1

Using the kinematic equation to solve the following problem,

Δx = v_{0 *} t + 1/2 * a* t²

^

v₀, initial velocity = 0 m/s

t = 7.75 sec

a = 47.0 m/s²

In this case, max height will be the displacement, Δx

Solving the above equation, we get

Δx =0+ 1/2 x 47.0 x 7.75²

Δx = 1411.47 m

Hence, the height that the rocket reaches above the surface is 1411.47 m.