physics
posted by neha .
A 100g golf ball moving with a velocity of 20 m/s, collides with an 8 kg steel ball at rest,if the collision is elastic,compute the velocities of both balls after the collision.

Both kinetic energy and momentum are conserved. Assume a headon collision with motion along the x axis only.
There is an easy way to do this without aq lot of algebra.
The centerof mass velocity is
Vcm = 0.1*20/8.1 = 0.2469 m/s
In a coordinate system travelling at Vcm, both balls reverse direction and keep the same speed.
Golf ball initial velocity in CM system = 20  0.2469 = 19.753 m/s
Golf ball final velocity in CM system = 19.753 m/s
Golf ball final velocity in lab coordinates = 19.753 +.2469 = 19.506 m/s
Steel ball initial velocity in CM coordinates = 0.2469 m/s
Steel ball final velocity in CM coordinates = +0.2469 m/s
Steel ball final velocity in lab coordinates = +0.4938 m/s
Check: Final KE = 0.98 + 19.02 = 20.00 J = Initial KE
Final momentum = 3.9504  1.9506 = 2.00 kg m/s = Initial momentum