Ice skaters collision with angle

[fantisism]

Homework Statement

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?

Homework Equations

m₁v_1ix+m₂v_2ix=m₁v_1fx+m₂v_2fx
m₁v_1iy+m₂v_2iy=m₁v_1fy+m₂v_2fy

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.

 

[ehild]

You have v1_fx and v1_fy in the equations for components of momentum. How do you get them, knowing magnitude and angle of velocity ?

 

[fantisism]

You have v1_fx and v1_fy in the equations for components of momentum. How do you get them, knowing magnitude and angle of velocity ?

Is v_1fx=(4 m/s)(cos(25°)) and v_1fy=(4 m/s)(sin(25°))?

 

[ehild]

Is v_1fx=(4 m/s)(cos(25°)) and v_1fy=(4 m/s)(sin(25°))?

Yes.

 

[fantisism]

Yes.

And then with that information, solve for v_2fx and v_2fy?

 

[ehild]

And then with that information, solve for v_2fx and v_2fy?

Yes.

 

[fantisism]

Yes.

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((v_2fx)²+(v_2fy)²? And that would be the answer for the first question?

 

[ehild]

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((v_2fx)²+(v_2fy)²? And that would be the answer for the first question?

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

 

[fantisism]

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

To find the angle, would it be arctan(v_2fy/v_2fx)?

 

[ehild]

To find the angle, would it be arctan(v_2fy/v_2fx)?

Yes.

 

[fantisism]

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