The eight ball, which has a mass of m = 0.5 kg, is initially moving with a velocity v = 4.7i m/s. It strikes the six ball inelastically, which has an identical mass and is initially at rest. After the collision the eight ball is deflected by an angle of θ = 19° and the six ball is deflected by an angle of Φ = 13°, as shown in the figure. a. Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the problem and the magnitude of the eight ball's initial velocity, v. (b)  What is the magnitude of the velocity, in meters per second, of the six ball? (c)  What is the magnitude of the velocity of the eight ball, in meters per second, after the collision?

Question
Asked Nov 7, 2019
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The eight ball, which has a mass of m = 0.5 kg, is initially moving with a velocity v = 4.7i m/s. It strikes the six ball inelastically, which has an identical mass and is initially at rest. After the collision the eight ball is deflected by an angle of θ = 19° and the six ball is deflected by an angle of Φ = 13°, as shown in the figure.

 

a. Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the problem and the magnitude of the eight ball's initial velocity, v.

 

(b)  What is the magnitude of the velocity, in meters per second, of the six ball?

 

(c)  What is the magnitude of the velocity of the eight ball, in meters per second, after the collision?

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Expert Answer

Step 1

Given:

Mass of the eight ball, m = 0.5 kg

Initial velocity of the eight ball, v = 4.7i m/s

Mass of the sixth ball, m = 0.5 kg

Initial velocity of the sixth ball, u2 = 0

Angle of deflection of eighth ball = 19ο

Angle of deflection of sixth ball = 13ο

Final velocity of the eight ball = v1

Final velocity of the sixth ball = v2

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19 8 13 6

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Step 2

Part (a): on applying the law of the conservation of momentum

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ту, + my, my+ mu, 3D тv, + mv, v +0 2 = 1

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Step 3

On applying the conservation of ...

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v=vcos0+v2cos .. (1)

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