Question

A 70.0-kg ice hockey goalie, originally at rest, has a 0.170-kg hockey puck slapped at him at a velocity of 43.5 m/s. Suppose the goalie and the puck have an elastic collision, and the puck is reflected back in the direction from which it came. What would the final velocities of the goalie and the puck be in this case? Assume that the collision is completely elastic.

Answer 1

Here we have to find final velocities of goalie and puck after the elastic collision.To solve this question we have to work with two equations

1. The total momentum of the system is a conserved

2. The total kinetic energy is a conserved

Let's start with the total momentum conservation i.e before and after the collision of goalie and puck the momentum is equal

Assume mass of goalie as m1 and puck as m2 and velocities as V (i and f denotes initial and final stage)

Equating momentum equation for elastic collision
m1 * Vi1 + m2* Vi2 = m1* Vf1 + m2 * Vf2 ----------(1)

Now, equating Kinetic energy equation for an elastic collision. Here, kinetic energy is conserved.
0.5*m1 * Vi1^2 + 0.5*m2* Vi2^2 = 0.5*m1* Vf1^2 + 0.5*m2 * Vf2^2...........(2)

Combining equation (1) and (2) we have

Vf1 = [(m1 - m2) Vi1 + 2 m2 Vi2 ]/[m1 + m2]

Vf2 = [2 m1 Vi1 ? (m1 - m2) Vi2]/[m1 + m2]

substituting the values from question

m1 = 70 kg
m2 = 0.170 kg
Vi1 = 0 m/s
Vi2 = 43.5 m/s

Vf1 = [(70 - 0.170) 0 + 2(0.170)43.5]/[70.170]

= 0.210 m/s (in the initial direction of the puck)

Now,

Vf2 = [0 ? (70 - 0.170)43.5]/[70.170] = -43.27 m/s (- sign means opposite direction)