Question

A 53.4 kg ice skater is at rest when she throws a snowball east at 14.8 m/s. The skater recoils west at 0.100 m/s. What is the mass of the snowball?

Answer 1

Answer:

0.36 kg

Explanation:

We can solve the problem by using the law of conservation of momentum: the total momentum at the beginning must be equal to the total momentum after the skater has thrown the ball.

Before the launch, the skater and the snowball are at rest, so the initial total momentum is zero:

$p_i = 0$

After the launch, the total momentum is:

$p_f = M V + m v$

where

M = 53.4 kg is the mass of the ice skater

v = -0.100 m/s is the velocity of the ice skater (here we assumed that east is the positive direction)

m is the mass of the snowball

v = +14.8 m/s is the velocity of the snowball

Since momentum must be conserved,

$p_i = p_f\\0 = MV +mv$

so we can find m:

$m=-\frac{MV}{v}=-\frac{(53.4 kg)(-0.100 m/s)}{14.8 m/s}=0.36 kg$