Answer to Question #91640 in Mechanics | Relativity for Marisol Cuevas

Question

A rocket climbs vertically and is powered in such a way that it has constant acceleration a. It reaches a height of 1km with a velocity of 100m/s. What is the value of a? How long does the rocket take to reach this 1km height?

Answer 1

Define height of rocket H = 1 km, velocity v = 100 m/s, time to reach 1 km t.

Since rocket has constant acceleration

$$H = v*t/2,$$

$$t=2*H/v=2*1000m/(100m/s)=20s$$

$$a=v/t=100m/s/(20s)=5m/s^2$$

Answer: a=5m/s², t=20s.