The bumper cars moving on a frictionless surface collide elastically. The first

Question

The bumper cars moving on a frictionless surface collide elastically. The first bumper car is moving to the right with a speed of 22.7 m/s and rear-ends the second bumper car, which is also moving to the right but with a speed of 5.27 m/s. What is the speed if the first bumper car after the collision? The mass of the first bumper car is 177 kg, and the mass of the second bumper car is 139 kg. Assume that the collision takes place in one dimension.
V (1f) = ------- m/s

Explanation / Answer

v2 - v1 = u1 - u2 v2-v1 = 22.7-5.27 = 17.43 v2 - v1 = 17.43 m/s------->(1) m1u1 + m2u2 = m1v1 + m2v2 177*22.7 + 139*5.27 = 177*v1 + 139*v2 177v1 + 139v2 = 4750.43-------->(2) solving equations (1) and(2) v1 = 7.366 m/s and v2 = 24.79m/s

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