a .105 kg hockey puck moving at 48 m/s is caught by a 75 kg goalie at rest. With what speed does the slide on the ice?
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To determine the speed at which the hockey puck and the goalie slide on the ice after the catch, we can use the principle of conservation of momentum. According to this principle, the total momentum before the catch should be equal to the total momentum after the catch.
The formula for momentum is given by:
Momentum = mass × velocity
Let's first calculate the total initial momentum before the catch. The momentum of the hockey puck is:
Momentum of the hockey puck = mass of the hockey puck × velocity of the hockey puck
Momentum of the hockey puck = 0.105 kg × 48 m/s
Next, let's calculate the total initial momentum of the goalie. Since the goalie is at rest initially, the momentum of the goalie is zero (assuming no other external forces acted on the goalie). Therefore:
Momentum of the goalie = 0 kg × 0 m/s
Now, let's calculate the total initial momentum before the catch:
Total initial momentum = Momentum of the hockey puck + Momentum of the goalie
Total initial momentum = (0.105 kg × 48 m/s) + (0 kg × 0 m/s)
= 5.04 kg·m/s
Since momentum is conserved, the total final momentum after the catch will also be 5.04 kg·m/s.
Let's assume the combined mass of the hockey puck and the goalie after the catch is M (in kg), and the final velocity is V (in m/s).
Total final momentum = Mass after the catch × Velocity after the catch
Total final momentum = M × V
Using the principle of conservation of momentum:
Total final momentum = Total initial momentum
M × V = 5.04 kg·m/s
Since the goalie is initially at rest and the hockey puck is caught by the goalie, the mass after the catch (M) will be the combined mass of the hockey puck and the goalie, which is 0.105 kg + 75 kg = 75.105 kg (approximately).
Substituting the values into the equation, we can solve for V:
75.105 kg × V = 5.04 kg·m/s
V = 5.04 kg·m/s / 75.105 kg
V ≈ 0.067 m/s (approximately)
Therefore, the puck and the goalie will slide on the ice with a speed of approximately 0.067 m/s after the catch.