Question

Sam (84.5 kg) and Alice (42.3 kg) stand on an ice rink, providing them with a nearly frictionless surface to slide on. Sam gives Alice a push, causing her to slide away at a speed (with respect to the rink) of 1.47 m/s.

With what speed does Sam recoil?

Answer 1

Sam recoils at a speed of 0.734 m/s in the opposite direction.

Step-by-step explanation:

The speed at which Sam recoils can be determined by applying the principle of conservation of momentum. In this case, the total momentum before the push is equal to the total momentum after the push. The momentum of an object can be calculated by multiplying its mass by its velocity.

Given that Sam's mass is 84.5 kg and Alice's mass is 42.3 kg, and that Alice slides away at a speed of 1.47 m/s, we can calculate Sam's recoil speed.

Momentum before = Momentum after

(Sam's mass * Sam's initial velocity) + (Alice's mass * Alice's initial velocity) = (Sam's mass * Sam's final velocity) + (Alice's mass * Alice's final velocity)

(84.5 kg * 0) + (42.3 kg * 0) = (84.5 kg * Sam's final velocity) + (42.3 kg * 1.47 m/s)

0 = (84.5 kg * Sam's final velocity) + (42.3 kg * 1.47 m/s)

Sam's final velocity = - (42.3 kg * 1.47 m/s) / 84.5 kg

Sam's final velocity = -0.734 m/s

Therefore, Sam recoils at a speed of 0.734 m/s in the opposite direction.