Reaction Time Physics│Please Help!

Question

A rocket is fired straight up with an initial velocity of 400m/s. How long will it take the rocket to reach the maximum height AND what is the maximum height.

Answer 1

The only force acting on the rocket is the force of gravity so the rocket will experience an acceleration of -9.8 m/s² in the downward direction,

At the peak of the rocket's travel, it will have an instantaneous velocity of 0 m/s

For constant acceleration:

v_f = v_i + at where vf = 0 m/s (top of the rocket's travel), vi = 400 m/s, a = -9.8 m/s2, and t = the time in seconds from launch to the peak of the rocket's travel

0 = 400 + (-9.8)(t)

-400 = -9,8t

-400/-9.8 = t

t = 40.816 or rounded, t = 41 s

Also for constant acceleration:

y = (1/2)at² + v_i(t)

y = (1/2)(-9.8)(40.816²) + (400)(40.816)

y = -8163 + 16327

y = 8163 or rounded, y = 8200 meters