Two billiard balls of equal mass move at right angles and meet at the origin of

Question

Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at vA = 1.6 m/s , and ball B is moving to the right along the x axis with speed vB = 4.0 m/s . After the collision, assumed elastic, ball B is moving along the positive y axis(Figure 1) .

Part A

What is the final direction of ball A?

Express your answer using two significant figures.

Part B

What are their two speeds?

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Explanation / Answer

mA = mB , vA =1.6 j m/s, vB =4i m/s,

from conservation of momentum along x direction

mAvAx+mBvBx= mAv'Ax+mBv'Bx

4 = v'Ax

from conservation of momentum along y direction

mAvAy+mBvBy= mAv'Ay+mBv'By

1.6 =v'Ay +v'By ..(1)

v'A = v'Ax^2 +v'Ay^2

for elastic collision kinetic energy is conserved

(1/2)mAvA^2+(1/2)mBvB^2 =(1/2)mAv'A^2+(1/2)mBv'B^2

1.6^2+4^2 = (4^2+v'Ay^2) + (v'By)^2 ...(2)

1.6 =v1 +v2

1.6^2+4^2 = (4^2+v1^2) + (v2)^2

v'Ay =0 , v'By =1.6 m/s

Part A:

direction of ball A is right along the x axis

Part B:

v'A = 4.0 m/s, v'B = 1.6 m/s

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