Question

On an ice skating rink, a girl of mass 50 kg stands stationary, facing a boy of mass 80 kg. They push off each other, and the boy moves away with a velocity of -4.0 m/s. What is the final velocity of the girl?

a) -2.5 m/s
b) -5.0 m/s
c) 2.5 m/s
d) 5.0 m/s

Answer 1

The final velocity of the girl can be calculated using the principle of conservation of momentum. Using the given masses and velocities, the final velocity of the girl is 6.4 m/s.

Step-by-step explanation:

The final velocity of the girl can be found using the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. In this case, the initial momentum of the system is zero since both the girl and the boy are initially stationary. After the collision, the momentum of the boy can be calculated using the formula:

momentum of boy = mass of boy * velocity of boy

Substituting the given values, we have:

momentum of boy = 80 kg * (-4.0 m/s) = -320 kg·m/s

Since the total momentum before and after the collision should be the same, the momentum of the girl can be calculated as:

momentum of girl = - momentum of boy

Substituting the calculated value of the momentum of the boy, we have:

momentum of girl = -(-320 kg·m/s) = 320 kg·m/s

The final velocity of the girl can be calculated using the formula:

final velocity of girl = momentum of girl / mass of girl

Substituting the given value of the mass of the girl and the calculated value of the momentum of the girl, we have:

final velocity of girl = 320 kg·m/s / 50 kg = 6.4 m/s