Question

A small rocket with mass 20.0 kg is moving in free fall toward the earth. Air resistance can be neglected. When the rocket is 80.0 m above the surface of the earth, it is moving downward with a speed of 30.0 m/s. At that instant the rocket engines start to fire and produce a constant upward force F on the rocket. Assume the change in the rocket's mass is negligible. What is the value of F if the rocket's speed becomes zero just as it reaches the surface of the earth, for a soft landing? (Hint: The net force on the rocket is the combination of the upward force F from the engines and the downward weight of the rocket.)

Answer 1

Answer:

= 308.5 N

Explanation:

acceleration  of rocket for safe landing

$v_{y} ^{2} = v_{0} ^{2} +2ay$

$a = \frac{v_{y}^{2} - v_{0}^{2} }{2y}$

$v_{0}$ = initial velocity

$v_{y}$ =final Velocity

m = mass of rocket

$\frac{0^{2} - 30^{2} }{2\times80}$

-5.625 $m/s^{2}$

Upward force

F - mg = ma

F = ma+ mg

F = m(a+g)

m= mass

a = 5.625 $m/s^{2}$

g = 9.8$m/s^{2}$

= 20(5.625 $m/s^{2}$+ 9.8$m/s^{2}$)

= 308.5 N