Question

question 10 of 26
an astronaut floating at rest in space has run out of fuel in her jetpack. she realizes that throwing tools from her toolkit in the opposite direction will help propel her back toward the space station. if the astronaut has a mass of 91 kg and she throws a hammer of mass 4 kg at a speed of 3.5 m/s, what will be the approximate resultant velocity that carries her back to the space station?
astronaut mass: 91 kg
hammer mass: 4 kg
a. 0.15 m/s
b. 0.05 m/s
c. 0.34 m/s
d. 0.10 m/s

Explanation:

Step1: Apply conservation of momentum

Initial momentum is 0. Let the velocity of the astronaut be $v$. According to the law of conservation of momentum $m_1v_1 + m_2v_2=0$, where $m_1 = 4$ kg, $v_1=3.5$ m/s and $m_2 = 91$ kg.

Step2: Solve for the astronaut's velocity

We have $4\times3.5+91\times v = 0$. Then $91v=- 4\times3.5$, and $v=-\frac{4\times3.5}{91}\approx - 0.15$ m/s. The negative sign just indicates the direction is opposite to the direction of the hammer's motion. The magnitude of the velocity is approximately $0.15$ m/s.

Answer:

A. 0.15 m/s