Final answer:
Using the conservation of momentum, the goalie slides at a speed of 0.074 m/s after catching the hockey puck on a frictionless surface.
Step-by-step explanation:
The student's question involves calculating the speed at which a goalie will slide on frictionless ice after catching a hockey puck. To find this speed, we can apply the law of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it. In this case, the initial momentum of the system (puck and goalie) is just the momentum of the moving puck since the goalie is initially at rest.
The initial momentum of the puck is the product of its mass and speed (0.111 kg × 50 m/s = 5.55 kg·m/s). Because there are no external forces and ice is frictionless, this momentum must be equal to the total momentum after the collision. When the goalie catches the puck, their combined mass is the sum of both masses, but the momentum is conserved:
Initial puck momentum = Final combined momentum
5.55 kg·m/s = (0.111 kg + 75 kg) × final speed
From this equation, we calculate the final speed to be:
Final speed = 5.55 kg·m/s / 75.111 kg
Final speed = 0.0739 m/s (rounded to the nearest thousandth)
Therefore, the goalie would slide on the ice at a speed of 0.074 m/s after catching the puck.