Final answer:
In an elastic collision between a stationary ice hockey goalie and a moving puck, the final velocity of the goalie is -0.105 m/s and the final velocity of the puck is 33.5 m/s, calculated using the conservation of momentum and kinetic energy.
Step-by-step explanation:
To determine the final velocities of the ice hockey goalie and the puck after an elastic collision, we can use the conservation of momentum and the fact that kinetic energy is also conserved in elastic collisions. The equations for conservation of momentum and kinetic energy for two objects in a one-dimensional collision are:
M1•V1i + M2•V2i = M1•V1f + M2•V2f
and
1/2•M1•V1i^2 + 1/2•M2•V2i^2 = 1/2•M1•V1f^2 + 1/2•M2•V2f^2
Where M1 and M2 are the masses of the goalie and the puck respectively, V1i and V2i are the initial velocities, and V1f and V2f are the final velocities. The goalie (mass = 70.0 kg) is initially at rest, so V1i = 0 m/s, and the puck (mass = 0.110 kg) is initially moving at V2i = -33.5 m/s (the negative sign indicates the initial direction towards the goalie).
Since the collision is elastic, the puck will rebound in the opposite direction it came from, hence its final velocity V2f will be positive. Applying the conservation of momentum and kinetic energy and solving for the final velocities, we find that:
V1f = (2•M2•V2i)/(M1 + M2)
V2f = V2i•((M1 - M2)/(M1 + M2))
Plugging in the values:
V1f = (2•0.110 kg•-33.5 m/s)/(70.0 kg + 0.110 kg) = -0.105 m/s (The goalie moves in the direction the puck came from)
V2f = -33.5 m/s•((70.0 kg - 0.110 kg)/(70.0 kg + 0.110 kg)) = 33.5 m/s (The puck moves back in the direction it was originally travelling)
So, the final velocity of the goalie is -0.105 m/s and the final velocity of the puck is 33.5 m/s.