Question

The eight ball, which has a mass of m=0.5kg, is initially moving with a velocity v=4.9i m/s. It the strikes the six ball, which has an identical mass and is initially at rest. After the collision the eight ball is deflected by an angle of theta 27 degrees and the six ball is deflected by an angle psi 31 degrees. (a) Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the eight ball's initial velocity, v.

Answer 1

given

m = 0.5kg

v = 4.9i m/s

= 27 degrees

= 31 degrees

m₁v₁ ( i + 0 ) = m₁v₁'( cosi + sinj ) + m₂v₂' ( cosi - sinj )

m₁ = m₂  

v₁ ( i + 0 ) = v₁'( cosi + sinj ) + v₂' ( cosi - sinj )

v₁ = v₁' cos + v₂' cos

0 = v₁'sin - v₂' sin

then

v₂' = v₁ / ( sincos / sin + cos )

v₂' = 4.9 / ( sin31cos27 / sin27 + cos31 )

v₂' = 2.57 m/sec

v₁' = v₂' sin / sin

v₁' = 2.57 X sin31 / sin27

v₁' = 2.91 m/sec