A 700- kg car collides with a 1500- kg car that was initially at rest at the ori

Question

A 700- kg car collides with a 1500- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 15.0 km/h in a direction of 35 o with respect to the positive x axis. The heavier car moves at 18 km/h at -46 o with respect to the positive x axis. What was the initial speed of the lighter car (in km/h)? What was the initial direction (as measured counterclockwise from the x-axis)?

I was able to find the the V1=43.751km/h but can not seem to answer the angle correctly

A 700- kg car collides with a 1500- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 15.0 km/h in a direction of 35 o with respect to the positive x axis. The heavier car moves at 18 km/h at -46 o with respect to the positive x axis. What was the initial speed of the lighter car (in km/h)? What was the initial direction (as measured counterclockwise from the x-axis)? I was able to find the the V1=43.751km/h but can not seem to answer the angle correctly

Explanation / Answer

form momentum conservation,

700 x v = 700 x15 (cos35 i + sin35 j) + 1500 x 18(cos46i - sin46j)

V = 39.08 i - 19.14 j

magnitude= sqrt(39.08^2+ 19.14^2 ) = 43.52 km/h

angle = tan-1(-19.14 / 39.08) = -26.10 degrees

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