A 800- kg car collides with a 1500- kg car that was initially at rest at the ori

Question

A 800- 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 25.0 km/h in a direction of 25 o with respect to the positive x axis. The heavier car moves at 28 km/h at -43 o with respect to the positive x axis. The initial speed of the lighter car is 66.1 km/h. What was the initial direction (as measured counterclockwise from the x-axis)?

The correct answer is 337.5 degrees. Please explain step-by-step how to arrive at this answer.

Explanation / Answer

let the car m1 move at an angle a from the x-axis in the clockwise direction

conserving the momentum in x-direction

m1u1cos a + 0 = m1v1 cos 25 + m2v2 cos 43

800*66.1*5/18 * cos a = 800*25*5/18 cos 25 + 1500*28*5/18 * cos 43

cos a = 0.92

a = 22.53 degree from the x-axis in clockwise direction

angle in the counterclockwise direction = 360 - 22.53 = 337.46 degree

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