80.00 kg man catches a puck moving at 20 m/s, man is initially at rest. Man and puck move together after collision. The pucks mass is 0.16 kg, what is the final velocity?

0.04 m/s

dalezone

To solve this question, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Before the collision, the man is at rest, so his initial momentum is zero. The momentum of the puck is given by the product of its mass (0.16 kg) and its initial velocity (20 m/s):

Momentum of the puck before the collision = mass of the puck × initial velocity of the puck
= 0.16 kg × 20 m/s
= 3.2 kg·m/s

After the collision, the man and the puck move together, so their final velocity will be the same. Let's call this final velocity V.

The momentum of the man and the puck after the collision is the sum of their individual momenta:

Momentum of the man and the puck after the collision = (mass of the man + mass of the puck) × final velocity
= (80.00 kg + 0.16 kg) × V
= 80.16 kg × V

According to the principle of conservation of momentum, the initial momentum (zero) is equal to the final momentum:

Initial momentum = Final momentum
0 = 80.16 kg × V - 3.2 kg·m/s

Simplifying the equation:

80.16 kg × V = 3.2 kg·m/s
V = 3.2 kg·m/s / 80.16 kg

Calculating the final velocity:

V ≈ 0.0399 m/s

So, the final velocity of the man and the puck together is approximately 0.0399 m/s.

Note: The final velocity is positive, indicating that the direction of motion is the same as the initial velocity of the puck.