Question

A 58-kg ice skater moves across the ice at a constant speed of 2.0 m/s. She is caught by her 69-kg partner, and then the pair continues to glide together. He is at rest when he catches her, and immediately afterward they both coast. Even though the "magnitude of the change in momentum" is requested, you should provide a negative sign if the final momentum is less than (or more negative) than the initial momentum.

a. What is their velocity just after the catch? Assume she moves in the positive x-direction before her partner catches her.
b. A skater follows the girl at a constant speed of 1.0 m/s. What is the magnitude of the girl's change in momentum in the reference frame of the skater?

Answer 1

a. 0.91 m/s

b. -63.22 kg.m/s

Step-by-step explanation:

The principle of conservation of momentum states that the total momentum before collision is equal to the total momentum after collision in an isolated system.

If we assume the collision is isolated, then the total initial momentum is the sum of the momentum of the girl and that of the partner. Since the partner was at rest, his initial momentum is 0.

After collision, both glided with the same velocity which is in the direction of the girl's initial velocity.

`m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2`

Quantities with subscript 1 are for the girl and those with 2 are for the partner.
`m` represents mass,
`u` represents initial velocity and
`v` represents final velocity. Since the final velocities are the same,

`m_1u_1 + m_2u_2 = (m_1 + m_2)v`

where
`v` is the common velocity

Substitute known quantities.

`58*2 + 69*0= v(58+69)`

`116=69v`

`v=0.91`

b. With respect to the skater, the girl's initial velocity =
`u=2-1=1`

And the final velocity =
`v=0.91-1=-0.09`

Change in momentum =
`mv-mu=m(v-u)`

`58(-0.09-1)=58*-1.09=-63.22`