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.

 

[Moetasim]

Angles can be tricky to work with, but with practice and understanding of the concepts, it will become easier. In this problem, we can use the law of conservation of momentum to solve for the final velocity of the two players. By setting up equations for the conservation of momentum in the x and y directions, we can solve for the final velocities in both directions. Using trigonometry, we can then find the magnitude and direction of the final velocity vector.

For the second problem, you are on the right track by using the conservation of kinetic energy. However, it seems like you may have made a mistake in your calculations. Double check your work and make sure you are using the correct units for mass and velocity. If you are still having trouble, try breaking down the problem into smaller steps and solving for the final velocity of the nail first, then using that to find the final kinetic energy. Keep practicing and you will get the hang of it!