Two hockey pucks of equal mass approach each other. puck 1 has an initial velocity of 20.0 m/s (S 45 E), and puck 2 has an initial velocity of 15 m/s (S 45 W). after the collision, the first puck is moving with a velocity of 10.0 (S 45 W). Determine the final velocity of the second puck and explain if the collision is elastic, perfectly inelastic or non-perfectly elastic.

The answer is 21m/s on an angle of S 31 E. You need to remember that forces and velocities are vectors, and as such, must be added or subtracted if they act in opposite directions... Try the question again but remember that in the x direction, the pucks were initially travelling in opposite directions.

To determine the final velocity of the second puck and classify the collision, we need to analyze the conservation of momentum and kinetic energy.

1. Conservation of momentum:
In an isolated system, the total momentum before the collision is equal to the total momentum after the collision.
Let's break down the initial velocities into their horizontal (x) and vertical (y) components:
Puck 1 initial velocity: 20.0 m/s (S 45 E)
Puck 1 x-component: 20.0 * cos(45°)
Puck 1 y-component: 20.0 * sin(45°)

Puck 2 initial velocity: 15 m/s (S 45 W)
Puck 2 x-component: 15 * cos(45°)
Puck 2 y-component: -15 * sin(45°) [Negative sign indicates the opposite direction]

The x-components of the initial velocities add up to zero since they have the same magnitude but opposite directions:
Puck 1 x-component = 20.0 * cos(45°)
Puck 2 x-component = 15 * cos(45°)

The y-components of the initial velocities add up to zero:
Puck 1 y-component + Puck 2 y-component = 20.0 * sin(45°) - 15 * sin(45°) = 0

Since there is no net momentum in the y-direction, we only need to consider momentum in the x-direction.

Total momentum before collision:
Puck 1 momentum: (mass of puck 1) * (Puck 1 x-component)
Puck 2 momentum: (mass of puck 2) * (Puck 2 x-component)

2. Conservation of kinetic energy:
For an elastic collision, the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision. For a perfectly inelastic collision, the total kinetic energy is not conserved. We'll compare the total kinetic energy before and after the collision to determine which category this collision falls into.

Let m be the common mass of both pucks. The kinetic energy (KE) is given by:
KE = 0.5 * m * (velocity)^2

Total kinetic energy before the collision:
Puck 1 KE: 0.5 * m * (20.0)^2
Puck 2 KE: 0.5 * m * (15)^2

Total kinetic energy after the collision:
Puck 1 KE: 0.5 * m * (10.0)^2
Puck 2 KE: 0.5 * m * (final velocity of puck 2)^2

Comparison of the total kinetic energies before and after the collision will help determine if it is elastic or inelastic.

3. Determine the final velocity of the second puck:
Using the conservation of momentum, we can equate the momentum before and after the collision to find the final velocity of the second puck:
(Puck 1 momentum) + (Puck 2 momentum) = (mass of puck 2) * (final velocity of puck 2)

4. Analyze the results:
- If the total kinetic energy before and after the collision are the same, the collision is elastic.
- If the total kinetic energy after the collision is less than the total kinetic energy before the collision, the collision is perfectly inelastic.
- If the total kinetic energy after the collision is greater than the total kinetic energy before the collision, the collision is non-perfectly elastic.

By calculating the values and comparing the total kinetic energies, you can determine if the collision is elastic, perfectly inelastic, or non-perfectly elastic.

25

For this question my answer keeps on coming to 25m/s but answer is 28.