Angle from force applied / Momentum question

[Kaln0s]

Homework Statement

Okay the first question is:

1. A hockey puck with mass 0.250 kg has initial velocity 3.00 i + 5.00 j m/s just before being hit by a hockey stick. The final velocity after the hit is -37.0 i + 25.0 j m/s. What was the magnitude of the impulse delivered by the stick to the puck, in kg m/s?

For this I just took the final velocity - initial and took the magnitude to get .250 sqrt[-40^2 + 20^2] = 11.18

Part two though I have no idea how to do.

2. What is the angle of the force applied to the hockey puck in the previous problem? The angle should be measured with respect to the positive x-axis in degrees.

below.

3. Is it possible for the total momentum of three particles to be zero, even though the momentum of the individual particles is not?

below.

Homework Equations

p= mv
Velocityf - Velocityi

The Attempt at a Solution

2. I'm not sure how to do this... I thought of just doing the y over x component 400/1600 = 1/4 = 45 degrees. I don't think that's right though because looking at the final velocity it looks like it will be in quadrant 2 maybe?

3. I said yes as long as they were in the same plane because they wouldn't be able to be expressed in terms of each other. (mostly need confirmation on this yes / no)

Thanks for your help!

 

[praharmitra]

2. you have the direction of the initial, final velocity, and you have also calulated the direction of the impulse. Draw a vector diagram and find any angle that is necessary.

 

[nlightner]

I would like to provide the following response to the content:

1. Your approach to finding the magnitude of the impulse delivered by the stick to the puck is correct. However, it would be helpful to show the calculation steps and units in your answer. The final answer should be 11.18 kg m/s.

2. To find the angle of the force applied to the hockey puck, you can use the dot product formula: θ = cos^-1 ((A•B)/(|A||B|)). In this case, A represents the initial velocity vector and B represents the change in velocity vector (final velocity - initial velocity). Once you calculate the dot product, take the inverse cosine and convert the angle to degrees. This will give you the angle of the force with respect to the positive x-axis. In this case, the angle is approximately 118.7 degrees.

3. Your answer for the third question is correct. As long as the three particles are in the same plane and their momenta cancel out, the total momentum can be zero even if the individual momenta are not. This is known as conservation of momentum, which states that the total momentum of a system remains constant unless acted upon by an external force. So, in this case, the total momentum is zero because the forces acting on the particles cancel each other out.