Question

A 100-kg astronaut at rest is stranded from his space shuttle. He throws a 1-kg hammer away from the shuttle with a velocity of 13 m/s. With what speed will he be propelled toward the shuttle, in m/s? (Ignore the negative and round your answer to two decimal places if necessary. Assume the astronaut and the hammer together have a mass of

100+1)
[Hint: At the beginning, are the two masses together or are they apart?]

Answer 1

At the beginning, the astronaut and the hammer are together, so their total mass is 101 kg. According to the law of conservation of momentum, the total momentum of the system (astronaut + hammer) remains constant. Therefore, the momentum of the astronaut after throwing the hammer must be equal in magnitude and opposite in direction to the momentum of the hammer.

Let v be the velocity of the astronaut after throwing the hammer. We can use the conservation of momentum to find v:

(initial momentum) = (final momentum)

(101 kg)(0 m/s) = (100 kg + 1 kg)(v) + (1 kg)(13 m/s)

Simplifying this equation, we get:

0 = 101v + 13

Solving for v, we get:

v = -13/101 m/s

Since we are only interested in the magnitude of the velocity, we can take the absolute value of v to get:

|v| = 13/101 m/s ≈ 0.13 m/s

Therefore, the astronaut will be propelled toward the shuttle with a speed of about 0.13 m/s.