Question

A 55 kg hard sphere moving horizontally at 18 m/s due east collides head-on with a 65 kg hard sphere moving horizontally at 25 m/s due west. Assuming that the collision is one-dimensional elastic collision determine the following. What are the final velocities of each sphere after the collision?

Answer 1

Suppose -

m1 = 55 kg, m2 = 65 kg

Take the east direction as positive so west direction will be negative.

Initial velocities of the two spheres -

v1 = 18 m/s, v2 = -25 m/s

Suppose the final velocities of the two spheres after the collision is v1' and v2'.

Since the collision is elastic, so the expression of the final velocities are -

v1' = [(m1 - m2) / (m1+m2)]*v1 + [2m2 / (m1+m2)]*v2

= [(55-65) / (55+65)]*18 + [2*65 / (55+65)]*(-25)

= [-10/120]*18 +[130/ 120]*(-25) = -1.5 - 27.08 = - 28.58 m/s

Negative sign shows that the direction of motion of m1 is towards west.

Now, v2' = [2m1 / (m1+m2)]*v1 - [(m1-m2) / (m1+m2)]*v2

= [2*55 / (55+65)]*18 - [(55-65) / (55+65)]*(-25)

= 16.5 - [-0.083]*(-25) = 14.42 m/s

Positive sign shows that the direction of motion of m2 is towards east.