# Ice skaters collision with angle

1. Apr 23, 2016

### fantisism

1. The problem statement, all variables and given/known data
Two ice skaters crash into each other. Before they collide, one of them (50 kg) is skating in a straight line at 5 m/s, the other (40 kg) is skating at 4 m/s in a straight line at 90 degrees to the 50 kg skater’s direction. After the collision, the 50 kg skater is moving at 4 m/s at an angle of 25 degrees relative to their original direction. Calculate the velocity of the 40 kg skater after the collision. Is the total kinetic energy constant?

2. Relevant equations
m1v1ix+m2v2ix=m1v1fx+m2v2fx
m1v1iy+m2v2iy=m1v1fy+m2v2fy

3. The attempt at a solution
I drew a diagram before collision and after collision. Really, all I need to know is where in the formula(s) would I need to include the angle and I SHOULD be able to figure it out from there.

2. Apr 23, 2016

### ehild

You have v1fx and v1fy in the equations for components of momentum. How do you get them, knowing magnitude and angle of velocity ?

3. Apr 25, 2016

### fantisism

Is v1fx=(4 m/s)(cos(25°)) and v1fy=(4 m/s)(sin(25°))?

4. Apr 25, 2016

### ehild

Yes.

5. Apr 25, 2016

### fantisism

And then with that information, solve for v2fx and v2fy?

6. Apr 25, 2016

### ehild

Yes.

7. Apr 25, 2016

### fantisism

And then once I figure out what those two velocities are, I would square them individually and take the square root of the sums? So, sqrt((v2fx)2+(v2fy)2? And that would be the answer for the first question?

8. Apr 25, 2016

### ehild

The final velocity is asked. It is a vector with magnitude and direction. I think the problem wants both the magnitude and angle.

9. Apr 25, 2016

### fantisism

To find the angle, would it be arctan(v2fy/v2fx)?

10. Apr 25, 2016

### ehild

Yes.

11. Apr 25, 2016

### fantisism

Alright. I can solve the second subquestion myself. Thank you again!