Answer to Question #24636 in Mechanics | Relativity for vignesh

Question

Two identical billiard balls undergoes an oblique collision initially one of the ball is stationary if the initially stationary ball after collision moves in a direction which makes an angle of 37 with direction of intial motion of the moving ball then the angle through which initially moving ball will be deflected is

Answer 1

The law of conservation of energy:
T0 = T1 + T2
T - kinetic energy, T = mv^2/2
Therefore (m1 = m2 ):
v0^2 = v1^2 + v2^2
The law of conservation of momentum:
p0 = p1 + p2
p= m*v
p0^2 = p1^2 + p2^2 + 2p1*p2*cos(alpha)
alpha - angle between p1 and p2
Therefore:
v0^2 = v1^2 + v2^2 + 2*v1*v2*cos(alpha)
From laws of conservations:
cos(alpha) = 0 => alpha = 90
the angle through which initially moving ball will be deflected is:
90 - 37 = 53
Answer: 53