Question

A figure skating team has two skaters. One skater, with M1=60kg, skates with a velocity of 4m/s toward another skater with a mass of M2=75kg, who is at rest with a velocity of 0m/s. The 60kg skater jumps into the 75kg skater's arms.

a.) What is the final velocity of the pair after they collide?

b.) What was the change in energy in the system for the collision? Where did the lost energy go, or where did any extra energy come from?

c.) Now the 75kg skater, tosses the 60kg skater away at 4m/s in the direction of their motion. What is the velocity of the 75kg skater now?

d.) Imagine that instead, the skater were tossed at 4m/s in the direction opposite to their motion. What is the velocity of the 75kg skater now?

Answer 1

a] By momentum conservation,

initial momentum = final momentum

m1u1 + m2u2 = (m1+m2)v

60*4+75*0 = (60+75)v

v = 60*4/135 = 1.778 m/s answer

b] change in energy = final energy - initial energy = 0.5*(m1+m2)v^2 - 0.5m1u1^2 = 0.5*135*1.778^2 - 0.5*60*4^2

= -266.6 J

Energy is lost as it goes in producing heat.

c] again, by momentum conservation, (m1+m2)v = m1v1 +m2v2

135*1.778 = 60*4 + 75*v2

v2 = 0 m/s answer

d] By momentum conservation, (m1+m2)v = m1v1 +m2v2

135*1.778 = -60*4 + 75*v2

v2 = [135*1.778+60*4]/75 =  6.4 m/s answer