Two bumper cars at the county fair are sliding toward one another (see figure be

Question

Two bumper cars at the county fair are sliding toward one another (see figure below). Initially, bumper car 1 is traveling to the east at 5.62 m/s, and bumper car 2 is traveling 60.0° south of west at 10.00 m/s. After they collide, bumper car 1 is observed to be traveling to the west with a speed of 3.17 m/s. Friction is negligible between the cars and the ground. (a) If the masses of bumper cars 1 and 2 are 594 kg and 613 kg respectively, what is the velocity of bumper car 2 immediately after the collision? (Express your answer in vector form. Enter your answer to at least three significant figures.)

Explanation / Answer

velocity of car 1 v1 = 5.62i m/s

of car2 v2 = 10(-cos60i - sin60j ) = - 5i - 8.66j m/s

velocity of car1 after collision v1f = - 3.17i m/s

velocity of car2 after collision v2f

using momentum conservatoon for collision,

594x 5.62i + 613( - 5i - 8.66j ) = 596 x -3.17i +   613v2f

v2f = 3.53i - 8.66j m/s

speed = sqrt(3.53^2 + 8.66^2) = 9.35 m/s

direction = tan^-1(8.66/3.53) = 67.82 deg south of east.

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