Question

A 5.0 kg red ball moving to the east at 9.0 m/s collides elastically head-on with a 10.0 kg green ball moving to the west at 3.0 m/s. What are the final velocities of both balls?

Answer 1

here,

mass of red ball , m1 = 5 kg

initial speed , u1 = 9 m/s

mass of green ball , m2 = 10 kg

initial speed of green ball , u2 = - 3 m/s

let their final velocities be v1 and v2

using conservation of momentum

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

5 * 9 - 10 * 3 = 5 * v1 + 10 * v2 ....(1)

and

using conservation of kinetic energy

0.5 * m * u1^2 + 0.5 * m2 * u2^2 = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

5 * 9^2 + 10 * 3^2 = 5 * v1^2 + 10 * v2^2 ....(2)

from (1) and (2)

v1 = - 7 m/s

v2 = 5 m/s

the final speed of red ball is 7 m/s to the west

the final speed of green ball is 5 m/s to the east