What Is the Mass and Initial Velocity of Car 1 After Collision?

[CandyApples]

Homework Statement

Two cars collide as shown. Car s1 is initially moving along the x-axis at speed v1 and car 2 is stationary. The final speed of car one is 10 m/s and goes 30 degrees north of x-axis. The mass of car 2 is 2000kg and goes 6 m/s at 44 degrees south of x-axis. What is the mass and initial velocity of car 1.

Homework Equations

P = mv

The Attempt at a Solution

Pxi = m1v1. Pxf = m1v1*cos(33) + m2v2cos(44), Pxf = m1v1*cos(33) + 12000*cos(44)

My next thought was to set the two equations equal to each other because of conservation of momentum, but that won't work because there are two unknowns. Is the Pxf equation set up correctly, and if so, is there a way in which I can eliminate a variable?

 

[kuruman]

You have to be careful when you set equations equal to each other. Here you have momentum conservation in two dimensions so you get two momentum conservation equations, one for the x-direction and one for the y-direction. You need to say

P_{x, before}=P_x,after

and

P_{y, before}=P_y,after

Momentum is a vector so its components in all directions need to be conserved and you can't mix x and y components together.

 

[CandyApples]

Ohhhh and since Py initial is zero and the mass/velcoity of car 2 is known as well as final v for car 1 this becomes much easier. Funny how problems become less challenging when I utilize both dimensions.

 

[kuruman]

You call it "funny", I call it "learning." Good luck.