Question

In an elastic collision, a 350 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 4.40 m/s and that of the trailing car is 6.50 m/s. Assuming that the mass of the drivers is much, much less than that of the bumper cars, what are their final speeds (in m/s)?

leading bumper car _? m/s

trailing bumper car _? m/s

Answer 1

from the momentum conservation

m*u1 + m*u2 = m*v1 + m*v2

u1 and u2 are initial speeds of both bumper cars.

v1 and v2 are final speeds of both bumper cars.

4.40 + 6.50 = v1 + v2

v1 + v2 = 10.9 .................eq1

In elastic collision we know that

e = cofficient of restitution = 1

e = (v2 - v2)/(u1 -u2)

1 =  (v2 - v1)/(u1 -u2)

u1 - u2 = v2 - v1

4.40 - 6.50 = v2 - v1

v1 - v2 = 2.1 ............eq2

by adding eq1 and eq2

2*v1 = 13

v1 = 6.5 m/s

v2 = 4.4 m/s