Question

In a pool game, the cue ball, which has an initial speed of 3.0 m/s, make an elastic collision with the eight ball, which is initially at rest. After the collision, the eight ball moves at an angle of 40° to the original direction of the cue ball. (a) Find the direction of motion of the cue ball after the collision. ° (from the original line of motion) (b) Find the speed of each ball. Assume that the balls have equal mass. m/s (cue ball) m/s (eight ball)

Answer 1

Step-by-step explanation:

Given

initial speed(u)=3 m/s

mass of each ball is m

Let the cue ball is moving in x direction initially

In elastic collision Energy and momentum is conserved

Let u be the initial velocity and
`v_1 , v_2` be the final velocity of 8 ball and cue ball respectively

`(mu^2)/(2)+0=(mv^2_1)/(2)+(mv^2_2)/(2)`

The angle after which cue ball is deflected is given by

`\theta _1=90-40=50^(\circ)`

Conserving momentum in x direction

`mu=mv_1cos40+mv_2cos50`

`3=v_1cos40+v_2cos50`

Along Y axis

`0+0=v_1sin40-v_2sin50`

`v_1sin40=v_2sin50`

substitute the value of
`v_1`

we get
`v_2=1.912 m/s`

`v_1=2.27 m/s`