Question

A 100 kg free-floating astronaut fires 0.1 kg of gas at a speed of 50.0 m/s from her propulsion pistol. What is the astronauts recoil speed?

Answer 1

The recoil speed of the astronaut is 0.05 m/s

Explanation:

We can solve the problem by using the law of conservation of momentum: in fact, the total momentum of the astronaut-gas system before and after must be equal.

Before, the total momentum is zero, since we consider them both at rest:

p = 0 (1)

After, the total momentum is:

$p=mv+MV$ (2)

where :

m = 0.1 kg is the mass of gas

v = 50.0 m/s is the velocity of the gas

M = 100 kg is the mass of the astronaut

V is the recoil velocity of the astronaut

Since momentum is conserved, we can equate the two equations, and we can find the recoil velocity of the astronaut:

$0=mv+MV\\V=-\frac{mv}{M}=-\frac{(0.1)(50.0)}{100}=-0.05 m/s$

where the negative sign means the astronaut will move backward, so the recoil speed is 0.05 m/s.

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