Answer:
To solve this problem, we can use the law of conservation of momentum, which states that the total momentum of a system is conserved in the absence of external forces. In this case, the system consists of the hockey puck and the goalie.
Before the catch, the momentum of the puck is:
puck momentum = m1 * v1 = 0.2 kg * 24 m/s = 4.8 kg m/s
where m1 is the mass of the puck and v1 is its velocity.
The momentum of the goalie before the catch is zero since the goalie is at rest.
After the catch, the combined momentum of the puck and the goalie is:
combined momentum = m1 * v2 + m2 * v3
where v2 is the velocity of the puck after the catch, v3 is the velocity of the goalie and m2 is the mass of the goalie with the equipment.
Since the system is closed and there are no external forces, the momentum is conserved. Therefore:
puck momentum = combined momentum
4.8 kg m/s = 0.2 kg * v2 + 75 kg * v3
Solving for v3, the velocity of the goalie after the catch, we get:
v3 = (4.8 kg m/s - 0.2 kg * v2) / 75 kg
We need to find v2, the velocity of the puck after the catch. Since the puck is caught and held, its velocity is zero.
Substituting v2 = 0 into the above equation, we get:
v3 = 4.8 kg m/s / 75 kg = 0.064 m/s
Therefore, the goalie (with the puck) slides on the ice with a speed of 0.064 m/s.