A 25.0 kg bumper car moving to the right at 5.00 m/s overtakes and col-

lides clastically with a 35.0 kg bumper car moving to the right. After the

collision, the 25.0 kg bumper car slows to 1.50 m/s to the right, and the

35.0 kg car moves at 4.50 m/s to the right.

a. Find the velocity of the 35 kg bumper car before the collision.

. b. Verify your answer by calculating the total kinetic energy before and

after the collision.

This problem bothers elastic collision.

Given data

Mass m1 = 25kg

Initial velocity u1 = 5m/s

Final velocity v1 = 1.5m/s

Mass m2 = 35kg

Initial velocity u2=?

Final velocity v2 = 4.5m/s

A. To find the initial velocity of the 35kg car, let us Apply the principle of conservation of energy

m1u1+m2u2 = m1v1+m2v2

25*5 + 35*u2 = 25*1.5 + 35*4.5

125+35u2 = 37.5+157.5

125+35u2=195

35u2 = 195-125

35u2 = 70

u2 = 2m/s

The initial velocity is 2m/s

B. Totally not kinetic energy before impact

KE = 1/2m1u1² + 1/2m2u2²

KE = (25*5²) / 2 + (35*2²) / 2

KE = 625/2 + 140/2

KE = 312.5+70

KE = 382.5J

Total kinetic energy after impact

KE=1/2m1v1² + 1/2m2v2²

KE = (25*1.5²) / 2 + (35*4.5²) / 2

KE = 56.25/2 + 708.75/2

KE=28.125 + 354.375

KE = 382.5J

We can see that energy is conserved

Kinetic energy before and after impact remains unchanged