Two billiard balls of identical mass move toward each other as shown in the figu

Question

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 v1i = +30.1 cm/s and v2i = -22.0 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.) v1f = cm/s v2f = cm/s Find the final velocity of the two balls if the ball with velocity v2i = -22.0 cm/s has a mass equal to half that of the ball with initial velocity v1i = +30.1 cm/s. (Indicate the direction with the sign of your answer.) v1f = cm/s vsf = cm/s

Explanation / Answer

v1f = (2 m2 v2 + (m1 - m2) v1)/(m1 + m2) = 2*m*-22/(2m) = -22 cm/s
v2f = (2 m1 v1 + (m2 - m1) v2)/(m1 + m2)= 2*m*30.1/2m = 30.1 cm/s

next case
v1f = (2 m2 v2 + (m1 - m2) v1)/(m1 + m2)= (m * -22 + m/2*30.1)/(3m/2) = -4.63 cm/s
v2f = (2 m1 v1 + (m2 - m1) v2)/(m1 + m2) = ( 2*m*30.1 + (-m/2)*-22)/(3m/2)=47.47 cm/s

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