In an elastic collision, a 580 kg bumper car collides directly from behind with a second, identical bumper car that is traveling in the same direction. the initial speed of the leading bumper car is 1.50 m/s and that of the trailing car is 2.75 m/s. assuming that the mass of each driver is 65 kg, what are the cars' final speeds after the collision? '

 vl = 2.75 m/s vt = 1.5 m/s

Explanation:

If we assume that no external forces act during the collision, total momentum must be conserved.

If both cars are identical and also the drivers have the same mass, we can write the following:

m (vi1 + vi2) = m (vf1 + vf2) (1)

The sum of the initial speeds must be equal to the sum of the final ones.

If we are told that kinetic energy must be conserved also, simplifying, we can write:

vi1² + vi2² = vf1² + vf2² (2)

The only condition that satisfies  (1) and (2) simultaneously is the one in which both masses exchange speeds, so we can write:

vf1 = vi2 and vf2 = vi1

If we call v1 to the speed of the leading car, and v2 to the trailing one, we can finally put the following:

vf1 = 2.75 m/s  vf2 = 1.5 m/s

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