How Do Angles Affect Momentum and Kinetic Energy in Physics Problems?

[Ms June Day]

Homework Statement

Two 75.0 kg hockey players skating at 5.90 m/s collide and stick together. If the angle between their initial directions was 135°, what is their speed after the collision? (Let the motion of player 1 be in the positive x-direction and the motion of player 2 be at an angle of 135° measured counterclockwise from the positive x-axis.)

also the answer is to be the velocity in the x direction, and the velocity in the y direction

Homework Equations

I've tried a bunch relating to momentum..

The Attempt at a Solution

I tried using trig, but there must be and easier way that I'm missing


ONE MORE:
The collision between a hammer and a nail can be considered to be approximately elastic. Estimate the kinetic energy acquired by a 11 g nail when it is struck by a 550 g hammer moving with an initial speed of 4.9 m/s.

I know that KE = .5mv^2 and that this is elastic, therefore the initial KE must equal the final KE. I got 2.4, which seems close, but still incorrect.

 

[MarkusNaslund19]

For the hockey question, do use trig. Break the velocities for both players into vertical and horizontal components.

For the player going in the x-direction: p_x = mv

For the other player: p_x = -mvcos45 and p_y = mvsin45

Also, remember that momentum is conserved for both the horizontal and vertical directions. Vertically,

mvsin45 = (m+m)v_after.

Do the same for the horizontal component. I've probably done too much as it is.