A hockey puck with a mass of 0.18 kg travels at a velocity of 40 m/s toward a goalkeeper. The goalkeeper has a mass of 120 kg and is at rest. Assuming a closed system, find the total momentum of the puck before the puck is caught by the goalkeeper. -5.3 kg.m/s
0 kg.m/s
6.4 kg.m/s
7.2 kg.m/s
The total momentum of a closed system remains constant. Therefore, the total momentum of the puck before it is caught by the goalkeeper is equal to the total momentum of the goalkeeper and the puck after the catch.
Initial momentum of the puck = mass x velocity = 0.18 kg x 40 m/s = 7.2 kg.m/s
Since the goalkeeper is initially at rest, the initial momentum of the goalkeeper is 0 kg.m/s.
Therefore, the total initial momentum in the system is 7.2 kg.m/s.
After the puck is caught by the goalkeeper, they move together with a combined mass of 0.18 kg + 120 kg = 120.18 kg. Let's assume they move together with a final velocity v.
Conservation of momentum: initial momentum = final momentum
Total initial momentum = Total final momentum
7.2 kg.m/s + 0 kg.m/s = 120.18 kg x v
7.2 kg.m/s = 120.18 kg x v
v = 7.2 kg.m/s ÷ 120.18 kg
v ≈ 0.06 m/s
Therefore, the total final momentum is:
Total final momentum = 120.18 kg x 0.06 m/s = 7.21 kg.m/s
Since the momentum is conserved in a closed system, the total momentum of the puck before the catch is equal to the total momentum after the catch, which is 7.21 kg.m/s.
Therefore, the correct answer is 7.2 kg.m/s.