# Solving a Hockey Puck Collision: Final Velocity

• Veronica_Oles
In summary: However, even when I tried that, I still couldn't get 1.8 m/s. I got 1.77, which is close but not quite there. So either the solution is wrong, or there's some rounding error in the calculations. In summary, a hockey puck with a mass of 0.16kg and initial velocity of 2.0m/s[E] collides with another puck at rest with a mass of 0.17kg. After the collision, the first puck has a velocity of 1.5m/s[N 31 E] and the second puck has a final velocity of 1.7m/s[E 46 S]. The solution provided for the final velocity of the second puck is
Veronica_Oles

## Homework Statement

A hockey puck of mass 0.16kg has initial velocity of 2.0m/s[E] and collides with another puck that is initially at rest, has mass of 0.17kg. Once they collide the first puck travels 1.5m/s[N 31 E]. Find final velocity of second puck.

## The Attempt at a Solution

I keep getting an answer that does not match with solutions.

So I first drew it out then made a triangle that does is not a right angle, so I decided to use cosine law.
I am aware that my total momentum is 0.32 kg m/s because PT=PT' ...

PT= (0.16)(2)
=0.32 kg m/s

I also figured out my P1

P1= (0.16)(1.5)
= 0.24 kg m/s

I set my triangle up to have a 59° because 90°-31°.

Now I use cosine law to find opposite side of my 59°.

a=√(0.32)2+(0.24)2-2(0.24)(0.32)cos59
P2= 0.2844 kg m/s

Now I plug this into P=mv

V = 0.2844/0.17
V = 1.7m/s [E 46 S]

Did I do something wrong??

I worked this problem pretty quickly so like all of my solutions, I don't have a lot of confidence in it. But I got the same answer as you did. Maybe we both did it wrong the same way, or possibly the solution is wrong. Hopefully someone else will chime in.

Edit: I just worked the problem a second time and got the same result.

Last edited:
Veronica_Oles
I get the same. Do you know what the answer is supposed to be?

haruspex said:
I get the same. Do you know what the answer is supposed to be?
1.8 m/s. Which is close but usually the answer I get is the exact same as solutions.

Veronica_Oles said:
1.8 m/s. Which is close but usually the answer I get is the exact same as solutions.
I got 1.67, so 1.8 definitely seems wrong. Equal masses gives 1.77.
I varied the angle from 31 degrees. Had to take it down to about 25 to get 1.8m/s. (The second puck's angle was then 45 degrees S of E.)

Veronica_Oles and TomHart
@haruspex, I think you're right that they probably solved it using the same mass for both pucks.

Veronica_Oles

## 1. How do you calculate the final velocity of a hockey puck after a collision?

The final velocity of a hockey puck after a collision can be calculated using the formula vf = (m1v1 + m2v2)/(m1 + m2), where vf is the final velocity, m1 and m2 are the masses of the two colliding pucks, and v1 and v2 are their initial velocities.

## 2. Can you explain the conservation of momentum in a hockey puck collision?

According to the law of conservation of momentum, the total momentum before a collision is equal to the total momentum after the collision. In a hockey puck collision, this means that the combined mass and velocity of the two pucks before the collision is equal to the combined mass and velocity after the collision.

## 3. What factors can affect the final velocity of a hockey puck after a collision?

The final velocity of a hockey puck after a collision can be affected by factors such as the masses of the pucks, the angle at which they collide, the surface on which they are colliding, and the coefficient of restitution, which is a measure of how bouncy the surface is.

## 4. How does the angle of collision affect the final velocity of a hockey puck?

The angle of collision between two hockey pucks can affect the final velocity of the pucks after the collision. If the pucks collide head on, the final velocity of both pucks will be equal. However, if the angle of collision is not 180 degrees, the final velocities will be different and can be calculated using vector addition.

## 5. Can the final velocity of a hockey puck after a collision be greater than the initial velocity?

No, according to the law of conservation of energy, the final velocity of a hockey puck after a collision cannot be greater than the initial velocity. This is because energy is conserved in a closed system, and any energy lost during the collision will result in a decrease in velocity.

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