Find the final velocity of the two balls if the ball with velocity v2i 21.3 cm/s

Question

Find the final velocity of the two balls if the ball with velocity v2i 21.3 cm/s has a mass equal to half that of the ball with initial velocity vii 3 +27.9 cm/s. Let the mass of the ball traveling at -21.3 cm/s be equal to 1/2m. The mass of the ball traveling at Vif 27.9 cm/s would then be equal to 1/2m. Write conservation of momentum in terms of m, 1/2m, and the initial and final velocities of the balls. Apply conservation of energy in the form of vii v21 (vif v2f). You have two equations and two unknowns, so you should be able to solve for the unknowns cm/s Let the mass of the ball traveling at -21.3 cm/s be equal to m. The mass of the ball traveling at v2f 27.9 cm/s would then be equal to 1/2m. Write conservation of momentum in terms of m, 1/2m, and the initial and final velocities of the balls. Apply conservation of energy in the form of wii v21 (vif v2f). You have two equations and two unknowns, so you should be able to solve for the unknowns cm/s

Explanation / Answer

mass of the first ball m1 =m
its intial velocity u1 = 27.9 cm/s
mass of the second ball
m2 =m/2
its initial velocity u2 = -21.3 cm/s
after solving equations of conservation of momentum
and conservation of kinetic energy
we get the final equations for V1 and V2 as follows
Consider The final velocity ofthe ball which is moving intially with velocity of
27.9 cm/s is V1
V1 = [(m1-m2/m1+m2)u1] +[2m2u2/(m1+m2)]
V1 =[(m-0.5m/m+0.5m)*27.9] + [2*0.5m*(-21.3)/(m+0.5m)]
V1 = [9.3]+[-14.2] = - 4.9 m/s
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Final velocity of the ball which is moving intially with -21.3 cm/s is V2

V2 =[(m2-m1/m1+m2)u2] + [2m1u1/(m1+m2)]
V2 =[(0.5m-m/m+0.5m)*(-21.3)] +[2*m*27.9/(m+0.5m)]
V2 = [7.1]+[37.2] = 44.3 cm/s
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