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## Homework Statement

Two balls of equal mass m undergo a collision, the velocities of the balls make angles of 25.5° and -45.9° relative to the original direction of motion of the moving ball.

(a) Draw and label a diagram to show the balls before and after the collision. Label the angles (something like alpha and beta)

(b)Calculate the final speeds of the balls if the initial ball had a speed of 3.63 m/s.

**[Answer:2.75 m/s and 1.65 m/s]**

## Homework Equations

Momentum Is Conserved in both X & Y Direction

X-Direction

m

_{1}v

_{i1x}+ m

_{2}v

_{i2x}= m

_{1}v

_{f1x}+ m

_{2}v

_{f2x}

Y-Direction

m

_{1}v

_{i1y}+ m

_{2}v

_{i2y}= m

_{1}v

_{f1y}+ m

_{2}v

_{f2y}

## The Attempt at a Solution

(B)

X-DIRECTION

Mass 1= Mass 2= M

m

_{1}v

_{i1x}+ m

_{2}v

_{i2x}= m

_{1}v

_{f1x}+ m

_{2}v

_{f2x}

[STRIKE](m)[/STRIKE]v

_{i1x}+ [STRIKE](m)[/STRIKE]v

_{i2x}= [STRIKE](m)[/STRIKE]v

_{f1x}+ [STRIKE](m)[/STRIKE]v

_{f2x}

v

_{i1x}+ v

_{i2x}= v

_{f1x}+ v

_{f2x}

(3.63 m/s [forward]) + 0 m/s = v

_{f1}cos∅ + v

_{f2}cos∅

(3.63 m/s [forward]) = v

_{f1}cos∅ + v

_{f2}cos∅

3.63 m/s = v

_{f1}cos25.5° - v

_{f2}cos45.9°

**EQUATION 2**

Y-DIRECTION

Mass 1= Mass 2= M

m

_{1}v

_{i1y}+ m

_{2}v

_{i2y}= m

_{1}v

_{f1y}+ m

_{2}v

_{f2y}

[STRIKE](m)[/STRIKE]v

_{i1y}+ [STRIKE](m)[/STRIKE]v

_{i2y}= [STRIKE](m)[/STRIKE]v

_{f1y}+ [STRIKE](m)[/STRIKE]v

_{f2y}

v

_{i1y}+ v

_{i2y}= v

_{f1y}+ v

_{f2y}

0 m/s + 0 m/s = v

_{f1}cos∅ + v

_{f2}cos∅

0 = v

_{f1}sin∅ + v

_{f2}sin∅

0 = v

_{f1}sin25.5° - v

_{f2}sin45.9°

v

_{f2}sin45.9° = v

_{f1}sin25.5°

v

_{f2}sin45.9° / sin25.5° = v

_{f1}

**EQUATION 1**

SUBSTITUTION 1 INTO 2

3.63 = [v

_{f2}sin45.9° / sin25.5°] cos25.5° - v

_{f2}cos45.9°

===================

Now I would have to Re-Arrange one of them and for either vf1 or vf2 and substitute, but when I do it I get a wrong answer (I think I may be entering the angles wrong)

Can Someone please do this question and check if they get the answers they should of Answer:2.75 m/s and 1.65 m/s

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