Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded,"floating" 100 m from the mothership.She suddenly throws her 2.00-kg wrench at 20 m/s in a direction away from the ship.If she and her spacesuit have a combined mass of 200 kg,how long does it take her to coast back to her spaceship?
A)1000 s
B)750 s
C)500 s
D)250 s
E)2.50 min

Question

Quizplus · Accepted Answer

First, we need to use conservation of momentum to find Jennifer's recoil velocity:
m_1v_1 = m_2v_2
(2.00 kg)(20 m/s) = (202.00 kg)v_2
v_2 = 0.198 m/s (velocity is negative since it is in the opposite direction of the wrench throw)

Next, we can use kinematic equations to solve for the time it takes Jennifer to coast back to her spaceship:
d = v_i t + (1/2)at^2
where d = 100 m (distance from spaceship), v_i = -0.198 m/s (Jennifer's recoil velocity), and a = -9.81 m/s^2 (acceleration due to gravity)
Solving for t:
100 m = (-0.198 m/s)t + (1/2)(-9.81 m/s^2)t^2
t = 500 s

Therefore, the best choice is C.

Astronaut Jennifer's Lifeline to Her Spaceship Comes Loose and She