A) Find the magnitude of the velocity of the interlocked vehicles after the coll

Question

A) Find the magnitude of the velocity of the interlocked vehicles after the collision.

B) What is the direction of motion of the interlocked vehicles after the collision? Give your answer in terms of the angle that the velocity vector makes with respect to East. (East = 0o, North = 90o, West = 180o, and South = 270o)

I need correct answers to Parts (A) & (B) in order to give full rating.

Two vehicles A and B are traveling west and south, respectively, toward the same intersection where they collide and lock together. Before the collision A (total weight 1870 N) is moving with a speed of 42 m/s and B (total weight 1100 N ) has a speed of 27 m/s. A) Find the magnitude of the velocity of the interlocked vehicles after the collision. B) What is the direction of motion of the interlocked vehicles after the collision? Give your answer in terms of the angle that the velocity vector makes with respect to East. (East = 0 degree, North = 90 degree, West = 180 degree, and South = 270 degree) I need correct answers to Parts (A) & (B) in order to give full rating.

Explanation / Answer

A) Applying momentum conservation

m1 u1 + m2 u2 = (m1 + m2) v

where v is the interlocked vehicles velocity

- (1870 * 42 ) i - (1100*27) j = (1870 + 1100) v

v =  - (1870 * 42/(1870 + 1100)) i - (1100*27/ (1870 + 1100)) j

v = ( - 26.44 i - 10 j ) m/s

magnitude of velocity of the interlocked vehicles = sqrt(26.44^2 + 10^2) = 28.267 m/s

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B) angle velocity vector makes with respect to East = 180 + tan-1(10/26.44) = 180 + 20.72

= 200.72 o

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