I am having trouble with the following problem. A 1600kg car traveling eastward

Question

I am having trouble with the following problem. A 1600kg car traveling eastward at 32 m/s collides at an intersection with a 700kg motorcycle traveling northward at 45 m/s. The two vehicles become entangled after the collision in the middle of the intersection. (A) What is the magnitude of the two vehicles velocity after the collision?
(B) What is the direction of both vehicles velocity after the collision?(measured clockwise from the east or positive x direction) (C) How much kinetic energy is lost by the two vehicles during the collision?

Explanation / Answer

(a)The mass of the car is m1 = 1600 kg The velocity of the car is v1 = 32i m/s The mass of the motorcycle is m2 = 700 kg The velocity of the motorcycle is v2 = 45j m/s
Let the magnitude of the two vehicles velocity after the collision be V We know from the relation m1v1 + m2v2 = (m1 + m2) * V or V = (m1v1 + m2v2/(m1 + m2)) (B)The direction of both vehicles velocity after the collision is tan? = (v2/v1) or ? = tan^-1(v2/v1) (measured clockwise from the east or positive x direction) (C)The kinetic energy lost by the two vehicles during the collision is K1 = (1/2)m1 * (V - v1)^2 and K2 = (1/2)m2 * (V - v2)^2

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