A 0.50 kg cue ball makes a glancing blow to a stationary 0.50 kg billiard ball. After the collision the cue ball deflects with a speed of 1.2 m/s at an angle of 30.0° from its original path. Calculate the original speed of the cue ball if the billiard ball ends up travelling at 1.6 m/s.

Answer 1

A 0.50 kg cue ball makes a glancing blow to a stationary 0.50 kg billiard ball. After the collision the cue ball deflects with a speed of 1.2 m/s at an angle of 30.0° from its original path. Calculate the original speed of the cue ball if the billiard ball ends up travelling at 1.6 m/s.

physics - bobpursley, Wednesday, June 4, 2014 at 10:47pm

I think you can safely assume conservation of energy.

1/2 .5 V^2=1/2 .5 1.2^2 + 1/2 .5 1.6^2
solve for V

Answer 2

sin(30) = sin(a)
(.5)(1.6) (1.2)(.5)

sin(30)(.6) = sin(a)(.8)
sin(a)= (sin(30)(.6))/.8
sin(a)= .375
a= 22.024º

Therefore, b= equals:
180º- 22.024º- 30º = 127.976

sin(30) = sin(127.976)
(.5)(1.6) (.5)(v)

sin(30)(.5)(v) = sin(127.976)(.5)(1.6)
v = (sin(127.976)(.5)(1.6))/ (sin(30)(.5))
v= .6306148577 / .25
v= 2.522m/s

The cue ball original speed is 2.5 m/s.