Question

A 50-kg ice skater is holding a 3-kg ball, moving at a steady +5 m/s. She then throws the ball backwards

at -10 m/s, if so what would her final velocity be?

Answer 1

Answer: 5.9 m/s

Step-by-step explanation:

This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum
`p_(o)` must be equal to the final momentum
`p_(f)`:

`p_(o)=p_(f)` (1)

Where:

`p_(o)=(m_(1)+m_(2))V_(o)` (2)

`p_(f)=m_(1)U_(f)+m_(2)V_(f)` (3)

`m_(1)=50 kg` is the mass of the skater

`m_(2)=3 kg` is the mass of the ball

`V_(o)=5 m/s` is the initial velocity of the skater and the ball

`V_(f)=-10 m/s` is the final velocity of the ball

`U_(f)` is the final velocity of the skater

Substituting (2) and (3) in (1):

`(m_(1)+m_(2))V_(o)=m_(1)U_(f)+m_(2)V_(f)` (4)

Isolating
`U_(f)`:

`U_(f)=((m_(1)+m_(2))V_(o)-m_(2)V_(f))/(m_(1))` (5)

`U_(f)=\frac{(50 kg+3 kg)5 m/s}-(3 kg)(-10 m/s)}{50 kg}` (6)

Finally:

`U_(f)=5.9 m/s`