PLEASE SHOW FORMULA USED, THANK YOU:) Problem 5: The eight ball m = 0.5 kg is in

Question

PLEASE SHOW FORMULA USED, THANK YOU:)

Problem 5: The eight ball m = 0.5 kg is initially moving with a velocity v = 2.9i m/s. It the strikes the six ball, which has an identical mass and is initially at rest. After the collision the eight ball is deflected by an angle of ? = 26 degrees and the six ball is deflected by and angle of ? = 33.5 degrees.

v = 2.9i m/s
? = 26 degrees
? = 33.5 degrees

(a) Write an expression for the magnitude of six ball's velocity.

(b) What is the magnitude in m/s?

(c) What is the magnitude of the velocity of the eight ball after the collision in m/s?

Explanation / Answer

a) momentum in the x

m vi = m veight cos(theta) + m vsix cos(phi)

in the y
0 = m veight sin(theta) - m vsix (sin phi)

veight = vsix sin(phi)/sin(theta)

vi = vsix sin(phi)/tan(theta) + v six cos(phi)



vsix = vi/(sin(phi)/tan(theta) + cos(phi))

b)
vsix = 2.9/(sin(33.5 degrees)/tan(26 degrees) + cos(26 degrees))= 1.43 m/s

c)

veight = 1.43*sin(33.5 degrees)/sin(26 degrees)= 1.8 m/s

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