Question

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 85
kg and she throws a hammer of mass 4.5 kg at a speed of 4 m/s, what will be
the approximate resultant velocity that carries her back to the space station?
Astronaut
mass:
85 kg
Hammer
mass
4.5 kg
-X
A. 0.21 m/s
B. 0.27 m/s
OC. 0.15 m/s
D. 0.41 m/s

Answer 1

By conserving momentum, the astronaut can propel herself back to the space station by throwing a hammer. Calculating the momentum of the hammer and equating it to the astronaut's momentum change gives a velocity of approximately A. 0.21 m/s for the astronaut.

Step-by-step explanation:

The astronaut realizes that by throwing tools from her toolkit in the opposite direction, she can propel herself back toward the space station. Conservation of momentum tells us that the momentum of the astronaut and the thrown hammer will be equal and opposite.

The astronaut's momentum change (Δp) is equal to the hammer's momentum (mass × velocity),

which is 4.5 kg × 4 m/s = 18 kg·m/s.

Because momentum is conserved, the momentum change of the astronaut must also be 18 kg·m/s.

To find the astronaut's velocity (v),

we'll use the formula Δp = m·v, where m is the mass of the astronaut and v is her velocity.

Therefore,

v = Δp/m = 18 kg·m/s / 85 kg, which calculates to approximately 0.21 m/s.