Question

On a test flight, a rocket with mass 400 kg blasts off from the surface of the earth. The rocket engines apply a constant upward force F until the rocket reaches a height of 100 m and then they shut off. If the rocket is to reach a maximum height of 400 m above the surface of the earth, what value of F is required? Assume the change in the rocket's mass is negligible.

Answer 1

Answer:F=11.76 kN

Explanation:

Given

mass of rocket $m=400 kg$

Force F is applied up to a height of 100 m then it is shut off

final velocity v up to which force is applied is given by

$v^2-u^2=2 as$

$v^2-0=2\times a\times 100$

$v=\sqrt{200 a}$

After this rocket continues to move to a maximum height under the action of gravity

using

$v_1^2-v^2=2 gs_2$

$s_2=400-100=300 m$

$0-200 a=-2\times 9.8\times 300$

$a=3 g=3\times 9.8=29.4 m/s^2$

thus Force is $F=ma$

$F=400\times 29.4=11,760=11.76 kN$