Question

A cue ball makes a glancing blow to a stationary billiard ball so that the cue ball deflects with a speed of 1.4 m/s at an angle of 30.0 degrees from its original path. The collision is considered to be elastic and the masses are the same. Calculate the angle the billiard ball ends up moving in, with respect to the original direction of the cue ball.the initial velocity of the cue ball is 2.0m/s

Answer 1

Perfect, lets start

So fisrt, you have to divide the problem in two axis, X and Y. The momentum is conserved in both

Momentum x

`\begin{gathered} \sum_{n\mathop{=}0}^(\infty)Px=mv_(1x)+mv_(0x)=mv_(2x)+mv_(3x) \\ m(2m/s)+m(0)=m(1.4\cdot\cos30)+mv_(3x) \\ 2=1.21+v_(3x) \\ v_(3x)=0.79m/s \end{gathered}`
`\begin{gathered} \sum_{n\mathop{=}0}^(\infty)Py=0=mv_(2y)+mv_(3y) \\ v_(2y)=v_(3y) \\ 1.4\cdot sin30=-v_(3y)=0.7m/s \end{gathered}`

Direction

`\tan^(-1)((-.7)/(.79))=-41.54\degree`

Magnitude

`√(-.7^2+.79^2)=1.056m/s`