Final answer:
To find the final velocity of a 74-kg goalie after catching a puck moving at 40 m/s, we apply the conservation of momentum. The final velocity of the goalie, considering an elastic collision, is approximately 0.0811 m/s in the direction of the puck's initial velocity.
Step-by-step explanation:
The question involves the conservation of momentum and the properties of an elastic collision. To find the final velocity of the 74-kg goalie after an elastic collision with a 0.150-kg hockey puck moving at 40 m/s, we can use the conservation of momentum formula:
m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'
where:
m1 = mass of the puck
v1 = initial velocity of the puck
m2 = mass of the goaltender
v2 = initial velocity of the goaltender (0 m/s since he's at rest)
v1' = final velocity of the puck
v2' = final velocity of the goaltender
For an elastic collision, the following also holds true:
v1 - v2 = -(v1' - v2')
Solving these equations simultaneously gives us the final velocities. In this case, since the goalie is significantly more massive than the puck, the resulting velocity for the goalie will be much smaller than the initial velocity of the puck, but in the same direction as the puck's velocity before the collision.
Substituting the given values, we obtain:
Assuming an ideally elastic collision and using the known masses and velocities, the specific calculation would be:
0.150kg * 40m/s + 74kg * 0 = 0.150kg * (-40m/s) + 74kg * v_goalie
This equation can be solved for v_goalie, which is the goalie's velocity after the collision:
v_goalie ≈ 0.0811 m/s
Therefore, the final velocity of the goalie is approximately 0.0811 m/s in the direction of the puck's initial velocity.