A 1100- kg car collides with a 1400- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 20.0 km/h in a direction of 25 o with respect to the positive x axis. The heavier car moves at 23 km/h at -50 o with respect to the positive x axis.

Question

A 1100- kg car collides with a 1400- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 20.0 km/h in a direction of 25 o with respect to the positive x axis. The heavier car moves at 23 km/h at -50 o with respect to the positive x axis. 
What was the initial speed of the lighter car (in km/h)?

bobpursley · Answer

You cannot assume elastic equation. But you do have conservation of momentum in two directions (x, and y).
in x direction

1100v*cosTheta=1100*20Cos25+1400*23cos50

In the y direction
1100v*sinTheta=1100*20sin25 -1400*23sin50

You are looking for v.

so, in the y equation solve for
v*sinTheta.

In the x equation, solve for v*cosTheta.

then

v=sqrt((vcosTheta)^2+(vsinTheta)^2)