In a game of billiards, the cue ball is traveling eastward when it strikes a sec

Question

In a game of billiards, the cue ball is traveling eastward when it strikes a second ball that is initially at rest. After the collision, the cue ball moves at 4.41 m/s, 25.0 degree south of east, and the second ball's speed is 3.05 m/s. At what angle (north of east) does the second ball travel? Assume each ball has a mass of 162 g. What was the speed of the cue ball prior to the collision? Is the kinetic energy of the colliding balls conserved? (Ignore the rotation of the balls.) Incorrect Yes Correct: No NEW Anonymous 1 Reply I tried to use degrees as the units for the first part and it doesn't work...What units are we supposed to use?

Explanation / Answer

Here ,

after the collision ,

v1 = 4.41 * (cos(25) i - j * sin(25))

v2 = 3.05 * (cos(theta) i + j * sin(theta))

let the speed of the cue ball earlier is u

Using conservation of momentum in y direction

- 4.41 * sin(25) + 3.05 * sin(theta) = 0

solving for theta

theta = 37.7 degree

the angle made with the east direction is 37.7 degree

--------------------------------

speed of the cue ball is u

Using conservation of momentum

m * u = m *(4.41 * cos(25) + 3.05 * cos(37.7))

solving for u

u = 6.41 m/s

the speed of the cue ball prior to collision is 6.41 m/s

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