Collision and using x and y coordinates.

[Crusaderking1]

Homework Statement

You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sam, with mass 72.0 kg, is given a push and slides eastward. Abigail, with mass 54.0 kg, is sent sliding northward. They collide, and after the collision Sam is moving at 36.0 degrees north of east with a speed of 5.80 m/s and Abigail is moving at 15.0 degrees south of east with a speed of 8.80 m/s.

Part A:
What was the speed of each person before the collision?
Sam's speed:
Abigail speed:

Part B:
By how much did the total kinetic energy of the two people decrease during the collision?

Homework Equations

The momentum on initial x = momentum on final x

The momentum on initial y = momentum on final y

m1 = Sam, m2 = Abby
mv = momentum

The Attempt at a Solution

on x:
(72.0 kg)(unknown) + (54.0 kg)(0 m/s) = (72.0 kg)(5.80cos36)+(54.0 kg)(8.80 cos15)

on y:

(72.0 kg)(0)+(54.0 kg)(unknown) = (72.0 kg)(5.80sin36)+(54 kg)(8.80sin15)

Sam = 11.067 m/s
Abby = 6.823 m/s

I also need help for Part B.

Am I approaching this problem correctly? Thanks.

 

[Crusaderking1]

Alright, I know Sam's initial velocity is 11.1 m/s for sure.

I am doing something wrong when calculating Abby's initial velocity, but I'm not sure what.

I did do (72.0 kg)(11.1 m/s) = (54.0 kg)(initial velocity) and received 14.8 m/s.

I think this is right, however, I do not know how to calculate the answer the way I was suppose to(using y-coords).

 

[therealnihl]

Check your signs, but your equations look correct. Since you have two equations and two unknowns it is a solvable system of equations. If you need helping solving the system, I would use substitution or you could try elimination.

 

[Crusaderking1]

Check your signs, but your equations look correct. Since you have two equations and two unknowns it is a solvable system of equations. If you need helping solving the system, I would use substitution or you could try elimination.

When I re-did the y-coords, I found that if I took 90 degrees minus the degrees given, then I would get 14.8 m/s.

For example, sin15 should have been sin75, and sin 36 should have been sin56.

Does this seem alright?

 

[Crusaderking1]

I changed Abigail's final velocity to negative since it has direction. It worked.

Thanks therealnihl.