Answer to Question #13430 in Mechanics | Relativity for harisha

Question

A BALL A OF MASS m MOVING WITH A VELOCITY u1 collides HEAD ON WITH ANOTHER BALL B OF SIMILAR MASS MOVING WITH VELOCITY u2 . the COEFFICIENT OF RESTITUTION IS e . THE RATIO OF FINAL & INITIAL VELOCITIES OF THE BALL A IS

Answer 1

The coefficient of restitution is given by
C = (Vb - Va) / (Ua - Ub)
for
two colliding objects, where
Va is the final velocity of the first object
after impact
Vb is the final velocity of the second object after impact
Ua
is the initial velocity of the first object before impact
Ub is the initial
velocity of the second object before impact
Let the ratio of final and
initial velocities of the ball A is x.
u1f = u1 * x
e = (u2f - u1f) / (u1
- u2) = (u2f - u1 * x) / (u1 - u2)
x = (u2f - e * (u1 - u2)) / u1.