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A 0.060-kg tennis ball, moving with a speed of 4.0 m/s, has a head-on collision

ID: 1552689 • Letter: A

Question

A 0.060-kg tennis ball, moving with a speed of 4.0 m/s, has a head-on collision with a 9.5 times 10^-2-kg ball initially moving in the same direction at a speed of 3.3 m/s. Assuming a perfectly elastic collision, determine the speed of each ball after the collision. Enter your answers numerically separated by a comma. Express your answers using two significant figures. Determine the direction of tennis ball after the collision. The tennis ball moves in the direction of its initial motion. The tennis ball moves in opposite direction.

Explanation / Answer

Set up two equations, one stating that the total kinetic energy is the same before and after the collision, and one stating that the total momentum is the same before and after the collision. Then solve them for the velocities afterward.

I'll call the tennis ball ball number 1 and the other ball ball number 2.

total energy before = total energy after
1/2(0.060kg)(4.00m/s)^2 + 1/2(0.095kg)(3.3m/s)^2 = 1/2(0.060kg)(v1)^2 + 1/2(0.095kg)(v2)^2

0.48 + 0.517275 = 0.03(v1)^2 + 0.0475(v2)^2

0.997275 = 0.03(v1)^2 + 0.0475(v2)^2

total momentum before = total momentum after
(0.060kg)(4.00m/s) + (0.095kg)(3.3m/s) = (0.060kg)(v1) + (0.090)(v2)

0.24 + 0.3135 = 0.06(v1) + 0.095(v2)

0.5535 = 0.06(v1) + 0.095(v2)

v2 = 0.5535 - 0.06(v1) / 0.095

putting value of v2 in equ 1

0.997275 = 0.03(v1)^2 + 0.0475(0.5535 - 0.06(v1) / 0.095)^2

by solving equation you will get values of v1 and v2..,