with a velocity v = 4.6i m/s. It the strikes the six ball, which has an...

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with a velocity v = 4.6i m/s. It the strikes the six ball, whichhas an identical mass and is initially at rest. After the collisionthe eight ball is deflected by an angle of Î¸ = 26Â° and the six ballis deflected by an angle of Î¦ = 35Â°, as shown in the figure.
Part (a) Write an expression for the magnitude of six ball'svelocity, in terms of the angles given in the problem and themagnitude of the eight ball's initial velocity, v.
Part (b) What is the magnitude of the velocity, in meters persecond, of the six ball?
Part (c) What is the magnitude of the velocity of the eightball, in meters per second, after the collision?

Answer & Explanation Solved by verified expert

4.3 Ratings (945 Votes)

m1 = m = 0.5 kgÂ Â Â Â Â Â Â Â Â Â Â Â Â Â m2 = m = 0.5 kg

befor collision

v1 = 4.6iÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â v2 = 0

after collision

v1'x = v1'*cos26Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â v2'x = v2'*cos35

v1'y = v1'*sin26Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â v2'y = v2'*sin35

from momentum conservation

along y

Piy = Pfy

0 = m1*v1'y + m2*v2'y

v1'y = v2'y

v1'*sin26 = v2'*sin35

v1' = v2'*sin35/sin26......(1)

along x axis

Pix = Pfx

m1*v = m1*v1'x + m2*v2'x

v = v1'*cos26 + v2'*cos35.......(2)

using 1 in 2

v = v2'*sin35*cos26/sin26 + v2'*cos35

v*sin26 = v2'*sin35*cos26 + v2' *cos35*sin26

v*sin26 = v2'*sin(35+26)

v*sin26 = v2'*sin61Â Â Â Â Â Â <------answer

-------

part(b)

v2' = 4.6*sin26/sin61 = 2.3 m/s <------answer

part(c)

v1' = v2'*sin35/sin26

v1' = 3 m/s <<------answer

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