An 85.0 kg man playing hockey catches a puck moving at 25.0 m/s. The man is initially at rest. The man and the puck move together after the collision. The puck's mass is 0.16 kg. What is the final velocity?
A. 4.00 m/s
B. 1.00 m/s
C. 13.6 m/s
D. 0.05 m/s
.16*25=(85+.16)V
V=about 16*25/100*85=4/100=about .05
answer D
Well, if the man and the puck are moving together after the collision, it means they must have a common final velocity. To find this velocity, we can use the principle of conservation of momentum.
The initial momentum of the system is given by the mass of the man times his initial velocity, which is 0 (since he is initially at rest), plus the mass of the puck times its initial velocity.
So, the initial momentum is: (0 kg)(0 m/s) + (0.16 kg)(25.0 m/s) = 4.0 kg*m/s.
Since there is no external force acting on the system, the total momentum of the system must remain constant. Therefore, the final momentum is also 4.0 kg*m/s.
The final momentum is given by the mass of the man and the puck, which is (85.0 kg + 0.16 kg), times their final velocity, which we'll call Vf.
So, (85.0 kg + 0.16 kg)(Vf) = 4.0 kg*m/s.
Simplifying this equation gives: 85.16 kg(Vf) = 4.0 kg*m/s.
Dividing both sides by 85.16 kg gives: Vf = 4.0 kg*m/s / 85.16 kg.
After crunching the numbers, we get Vf ≈ 0.047 m/s.
But wait! The answer choices are all given in meters per second with two decimal places, so we need to round our answer. And since we're being precise, let's round to three decimal places.
So, the final velocity is approximately 0.047 m/s, which is closest to answer choice D: 0.05 m/s.
To find the final velocity of the man and the puck after the collision, we can use the law of conservation of momentum.
The initial momentum of the system, consisting of the man and the puck, is zero since the man is initially at rest. The final momentum of the system will be the sum of the momentum of the man and the momentum of the puck.
Initial momentum = 0
Final momentum = (mass of man * final velocity of man) + (mass of puck * final velocity of puck)
The mass of the man is 85.0 kg, the mass of the puck is 0.16 kg, and the initial velocity of the puck is 25.0 m/s.
Final momentum = (85.0 kg * final velocity of man) + (0.16 kg * final velocity of puck)
Since the man and the puck move together after the collision, their final velocities will be the same, so let's call the final velocity v.
Final momentum = (85.0 kg * v) + (0.16 kg * v)
According to the law of conservation of momentum, the initial momentum and the final momentum should be the same.
0 = (85.0 kg * v) + (0.16 kg * v)
Now, let's solve for v.
0 = (85.0 kg + 0.16 kg) * v
0 = 85.16 kg * v
Divide both sides by 85.16 kg:
0 / 85.16 kg = v
v = 0
Therefore, the final velocity of the man and the puck after the collision is 0 m/s.
The correct answer is D. 0.05 m/s.
To find the final velocity, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision:
The man is initially at rest, so his initial momentum (Pi) is zero: Pi = 0 kg·m/s since Pi = m1 * v1 and v1 = 0 m/s.
The puck's initial momentum (Ppuck) is given by: Ppuck = m2 * v2 = (0.16 kg) * (25.0 m/s) = 4.0 kg·m/s.
After the collision:
The man and the puck move together, so they have the same final velocity (vf).
The final momentum (Pf) is given by: Pf = (m1 + m2) * vf = (85.0 kg + 0.16 kg) * vf.
According to the conservation of momentum, Pi = Pf.
Therefore, 0 kg·m/s = (85.0 kg + 0.16 kg) * vf.
Solving for vf:
vf = 0 kg·m/s / (85.0 kg + 0.16 kg)
vf ≈ 0 kg·m/s / 85.16 kg
vf ≈ 0.00000589 m/s
Therefore, the final velocity is approximately 0.00000589 m/s, which is very close to 0. Hence, the correct answer is (D) 0.05 m/s.