Solve 2D Momentum Problem: 2000kg Caddy & 1000kg VW

[planauts]

Homework Statement

The stoplight had just changed and a 2000 kg Cadillac had entered the intersection, heading north at 3.0 m/s, when it was struck by a 1000 kg eastbound Volkswagen. The cars struck together and slid to a half, leaving skid marks angled 35 degrees north of east. How fast was the Volkswagen going just before the impact?

Homework Equations

The Attempt at a Solution

So basically what I did was divided into components.

x: (3)(2000) = (3000)*v_x
y: (v_vw)*(10000) = (3000)*v_y

v_x, v_y is the velocity (after collision) in the x and y direction, respectively, of both cars stuck together (since it is an inelastic collision).
v_vw is the initial velocity of the Volkswagen.

Now what I did was that the angle is 35 degrees north of east. So basically made a triangle and figured that tan(35) = (v_y)/(v_x). This means (v_x)*(tan35) = v_y.

Then, I simplified the component equations to get:
x: 2 = v_x
y: v_vw = 3*v_y

Then plugging in for v_y, I got: v_vw = 3(2)(tan35) = 4.2 m/s as the velocity of the volkswagen.

However, the answer key says 8.6 m/s. Could someone please help me out?


Thanks

 

[ehild]

What directions you call x and y?

ehild

 

[planauts]

Thanks!

I got it now, I should have drawn a reference frame with the axis or maybe I should have used the actual coordinate axis.

tan 35 = (v_x)/(v_y)
(v_y) = (v_x)/tan35

v_vw = 3*v_y = 3*2/tan35 = 6/tan35 = 8.6

Thanks again.