Question

Two skaters face one another and stand motionless, then push against each other on the ice. If one's mass is 55 kg and he moves to the left after the push at a velocity of 4.3 m/s, how fast was the other skater traveling after the push if her mass was 48 kg.​

Answer 1

4.9 m/s to the right

Step-by-step explanation:

We are going to use the conservation law of linear momentum to find her velocity. Initially, they are motionless so their initial total momentum is zero. Let's assume that anything moving to the left has a negative velocity and anything moving to the right has a positive velocity. We can write the conservation law of momentum as

`0 = M_mv_m + M_wv_w`

where

`M_m` = mass of the man = 55 kg

`v_m` = velocity of the man = -4.3 m/s

`M_m` = mass of the woman = 48 kg

`v_w` = velocity of the woman

`\Rightarrow 0 = (55\:\text{kg})(-4.3\:\text{m/s}) + (48\:\text{kg})v_w`

Solving for
`v_w,`

`v_w = \left(\frac{55\:\text{kg}}{48\:\text{kg}}\right)(4.3\:\text{m/s}) = 4.9\:\text{m/s}`

going to the right.