In a game of billiards, the player wishes to \'sink\" the target ball in the cor

Question

In a game of billiards, the player wishes to 'sink" the target ball in the corner pocket, if the angle to the corner pocket is 35 degree what angle is the cue ball deflected? Assume the collision is elastic. A billiard ball 'A' moving at 5 m/s strikes a stationary ball 'B' of the same mass. After the collision ball A moves at 4 m/s at an angle of37 degree with respect to the original line of motion. Assuming an elastic collision, find the magnitude of the final velocity v vector_Bf (m/s) of ball B. a. 3 m/s b. 4 m/s c. 5 m/s d. 6 m/s e. Others

Explanation / Answer

26)  Initial velocity = 5.00m/s (lets say this is in the x-component)

To do this question, we need to know that momentum is conserved, meaning the overall velocity of the two balls has to be the same before and after the collision.

After collision...

Ball A: 4.0m/s *cos 37 = 3.2 m/s (x-component)
4.0m/s * sin 37 = 2.41 m/s ( y-component)

Ball B (struck ball): 5 m/s - 3.2m/s = 1.8 m/s (x-component)
-2.41 m/s (y-component) note: it has to be in the opposite direction to conserve momentum

tan^-1(2.41/1.8) = 53.2 degrees
Struck ball's velocity = sqrt(1.8^2 + 2.41^2) = 3.0 m/s at 53.2 degree with respect to the original line of motion.

Hope you understand!

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