A hockey puck moving at 28 m/s is caught by an 80.00 kg man who was at rest. The man and the puck move together after the collision. The pucks mass is 0.16 kg. What is the final velocity?
To find the final velocity of the man and the puck after the collision, we can use the principle of conservation of momentum.
The momentum before the collision is equal to the momentum after the collision:
(mass of puck × velocity of puck) + (mass of man × velocity of man) = (mass of puck + mass of man) × (final velocity)
Let's substitute the given values into the equation:
(0.16 kg × 28 m/s) + (80.00 kg × 0 m/s) = (0.16 kg + 80.00 kg) × (final velocity)
4.48 kg·m/s = 80.16 kg × (final velocity)
Now we can solve for the final velocity:
(final velocity) = 4.48 kg·m/s / 80.16 kg
(final velocity) = 0.0559 m/s
Therefore, the final velocity of the man and the puck after the collision is approximately 0.0559 m/s.
To find the final velocity of the man and the puck after the collision, we can use the principle of conservation of momentum.
The law of conservation of momentum states that the total momentum of an isolated system remains constant before and after a collision. In this case, the man and the puck are the isolated system.
The momentum before the collision can be calculated by multiplying the mass of the hockey puck by its initial velocity:
Momentum before = mass of puck × initial velocity of puck
Momentum before = (0.16 kg) × (28 m/s)
Momentum before = 4.48 kg·m/s
Since the man was initially at rest, his momentum before the collision is zero.
Momentum before = mass of man × initial velocity of man
0 = (80.00 kg) × initial velocity of man
initial velocity of man = 0 m/s
The total momentum before the collision is the sum of the momenta of the puck and the man:
Total momentum before = Momentum before (puck) + Momentum before (man)
Total momentum before = 4.48 kg·m/s + 0 kg·m/s
Total momentum before = 4.48 kg·m/s
According to the law of conservation of momentum, the total momentum after the collision also remains constant. Therefore:
Total momentum after = Total momentum before
The total momentum after the collision can be calculated by multiplying the combined mass of the puck and the man by their final velocity:
Total momentum after = (mass of puck + mass of man) × final velocity
Total momentum after = (0.16 kg + 80.00 kg) × final velocity
Total momentum after = 80.16 kg × final velocity
Total momentum after = 80.16 kg·m/s × final velocity
Since the total momentum before and after the collision is the same, we can equate the two equations:
4.48 kg·m/s = 80.16 kg·m/s × final velocity
Dividing both sides of the equation by 80.16 kg·m/s:
final velocity = 4.48 kg·m/s / 80.16 kg·m/s
final velocity ≈ 0.056 m/s
Therefore, the final velocity, after the collision, is approximately 0.056 m/s.
m1 = 0.16 kg
m2 = 80kg
V1 = 28 m/s.
(m1+m2)*V = m1*V1
(0.16+80)V = 0.16*28
V = 4.48/(0.16+80) = 0.056 m/s.