Question

A model rocket is launched straight upward from the surface of the Earth at a speed of 50 m/s. If air resistance is negligible, what is the instantaneous velocity of the rocket the moment before it hits the ground?

Answer 1

The instantaneous velocity of the rocket the moment before it hits the ground is 50 m/s.

Step-by-step explanation:

Given;

initial velocity of the rocket, u = 50 m/s

Determine the maximum height reached by the rocket.

at maximum height reached by the rocket, the final velocity, v = 0

v² = u² -2gh

0 = 50² - 2(9.8)h

19.6h = 2500

h = 2500 / 19.6

h = 127.55 m

At maximum height, the time to reach ground is given by;

h = ¹/₂gt²

`t = \sqrt{(2h)/(g) } \\\\t = \sqrt{(2*127.55)/(9.8) }\\\\ t = 5.1 \ s`

Before the rocket hits the ground the final velocity will be maximum;

v = u + gt

v = 0 + 9.8 x 5.1

v = 50 m/s

Therefore, the instantaneous velocity of the rocket the moment before it hits the ground is 50 m/s.