Two billiard balls move at right angles and meet at the origin. Ball A (the cue

Question

Two billiard balls move at right angles and meet at the origin. Ball A (the cue ball, 175 g) is initially moving upward along the y axis at vA = 2.0 m/s, and ball B (a numbered ball, 155 g) is moving to the right along the x axis at vB = 3.7 m/s. After the collision, ball B is moving along the positive y axis at 2.85 m/s.

What is the final velocity & direction of Ball A?

Two billiard balls move at right angles and meet at the origin. Ball A (the cue ball, 175 g) is initially moving upward along the y axis at vA = 2.0 m/s, and ball B (a numbered ball, 155 g) is moving to the right along the x axis at vB = 3.7 m/s. After the collision, ball B is moving along the positive y axis at 2.85 m/s. What is the final velocity & direction of Ball A?

Explanation / Answer

Here ,

vA = 2 j m/s

vB = 3.7 i m/s

vB' = 2.85 j m/s

Now , Using conservation of momentum

vA*mA + vB*mB = vA'*mA + vB'*mB

2j * 175 + 3.7 i * 155 = vA'*175 + 2.85 j * 155

vA' = -0.52 j + 3.28 i m/s

hence ,

final velocity = sqrt(.52^2 + 3.28^2)

final velocity = 3.32 m/s

and angle = -arctan(.52/3.28)

angle = -4.36 dergee

Final velocity of A is 3.32 m/s at angle -4.360 with positive x -axis

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