PRACTICE IT Use the worked example above to help you solve this problem. Two bil

Question

PRACTICE IT Use the worked example above to help you solve this problem. Two billiard balls of identical mass move toward each other as shown in the figure. Assume that the collision between them is perfectly elastic. If the initial velocities of the balls are vii = +29.2 cm/s and V2,--21.3 cm/s, what are the velocities of the balls after the collision? Assume friction and rotation are unimportant. (Indicate the direction with the sign of your answer.) 1-21.3 2f29.2 cm/s cm/s EXERCISE HINTS: GETTING STARTED I I'M STUCK! Find the final velocity of the two balls if the ball with velocity v221.3 cm/s has a mass equal to half that of the ball with initial velocity V+29.2 cm/s. (Indicate the direction with the sign of your answer.) cm/s cm/s Need Help? Read It 921

Explanation / Answer

In a perfectly elastic collision

Using momentum conservation

Pi = Pf

m1V1i + m2V2i = m1V1f + m2*V2f

given that m1 = m & m2 = m/2

m*V1i + m*V2i/2 = m*V1f + m*V2f/2

2*V1i + V2i = 2*V1f + V2f

2*29.2 - 21.3 = 2*V1f + V2f

2*V1f + V2f = 37.1

Now In elastic collisions,

V1f - V2f = V2i - V1i

V1f - V2f = -21.3 - 29.2

V1f - V2f = -50.5

Now Solving both equation

Add both of them

3*V1f = 37.1 - 50.5

V1f = (37.1 - 50.5)/3 = -4.47 cm/sec

V2f = V1f + 50.5

V2f = -4.47 + 50.5 = 46.03 cm/sec

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