During a game of pool you hit the cue ball such that it stri

During a game of pool you hit the cue ball such that it strikes another ball sitting at rest. The cue ball grazes the striped ball so that the two fly off in opposing directions as shown below. The cue ball and the striped ball both have masses of 0.165 kg and the cue ball is initially given a speed of 2 m/s. If the cue ball recoils with an angle of theta_1=60 degrees and theta_2=30 degrees, find the following: total momentum of the system before the collision; total momentum of the system after the collision; the final speeds of each ball after the collision.

Solution

(a) total momentum of system before the collision,

pi = m1v1i + m2*0 = 0.165 x 2

= 0.33 kg m/s

(B) during collision, momentum of system doesn\'t change.

hence using momentum conservation,

momentum after collision= 0.33 kg m/s

(C) momentum after collision,

m1 v1f ( cos@1i - sin@1) + m2 v2f (cos@2i + sin@2j) = 0.33i

(v1fcos60 + v2fcos30)i + (v2fsin30 - v1fsin60)j = 2i + 0j

hence v2fsin30 - v1fsin60 = 0

v2f = 1.732v1f

along i vector,

v1fcos60 + (1.732v1f)cos30 = 2

v1f = 1 m/s .........Ans

v2f = 1.732 m/s .......Ans