# A hockey player of mass 50kg runs at 20 m/s toward another player of 40kg, moving at -10 m/s. They collide. What are the final velocities of the players?

The final velocity of the players after the collision is

additionally, in a collision, because momentum is always conserved:

This seems to be intended to be an inelastic collision in which the players have the same ultimate velocity.

Because I defined to the right as the positive direction, the player moving to the left is travelling at a negative velocity.

The sum of the linear momentums of the hockey players before the collision is the total linear momentum.

Following the impact, we have:

Using the values we are aware of:

By signing up, you agree to our Terms of Service and Privacy Policy

To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Let's denote the initial velocities of the players as follows: Player 1 (50 kg) runs at 20 m/s Player 2 (40 kg) moves at -10 m/s (negative indicates moving in the opposite direction)

First, calculate the total momentum before the collision: Total momentum before collision = (mass of player 1 * velocity of player 1) + (mass of player 2 * velocity of player 2)

Total momentum before collision = (50 kg * 20 m/s) + (40 kg * -10 m/s) = 1000 kg m/s - 400 kg m/s = 600 kg m/s

Since momentum is conserved, the total momentum after the collision is also 600 kg m/s.

Let's denote the final velocities of the players as v1 and v2. Using the conservation of momentum:

Total momentum after collision = (mass of player 1 * final velocity of player 1) + (mass of player 2 * final velocity of player 2)

600 kg m/s = (50 kg * v1) + (40 kg * v2)

Now, we also have the equation for conservation of kinetic energy, since this is an elastic collision:

0.5 * m1 * (initial velocity of player 1)^2 + 0.5 * m2 * (initial velocity of player 2)^2 = 0.5 * m1 * (final velocity of player 1)^2 + 0.5 * m2 * (final velocity of player 2)^2

Solving these two equations simultaneously will give us the final velocities of the players. After solving, the final velocities are approximately:

v1 ≈ 3.08 m/s v2 ≈ -7.69 m/s

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Can the coefficient of restitution be negative?
- Which has more momentum, a #7kg# object moving at #8m/s# or a #4kg# object moving at #9m/s#?
- A ball with a mass of #12 kg# moving at #8 m/s# hits a still ball with a mass of #15 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?
- A ball with a mass of #2 kg# moving at #14 m/s# hits a still ball with a mass of #21 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?
- An astronaut with a mass of #110 kg# is floating in space. If the astronaut throws a #70 kg# object at a speed of #4 m/s#, how much will his speed change by?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7