Question

Two rubber balls undergo an elastic collision. Ball 1 has a mass of 10 kg and an initial velocity of 5 m/s in the positive x direction. Ball 2 has a mass of 10 kg and is stationary. What is the final velocity of the two balls, v1f, and v2f?

Answer #1

Using conservation of momentum

m1v1i + m2v2i = m1v1f + m2v2f

as second ball was at rest, v2i = 0

m1v1i = m1v1f + m2v2f

from conservation of energy

m1v1i^{2} = m1v1f^{2} + m2v2f^{2}

Now, put in the values, we have

50 = 10*v1f + 10*v2f

divide by 10, we get

5 = v1f + v2f ------------ (1)

250 = 10*v1f^{2} + 10*v2f^{2}

divide by 10, we get

25 = v1f^{2} + v2f^{2} --------------(2)

solve for v1f from momentum equation (1)

v1f = 5 - v2f

put this in (2)

25 = (5 - v2f)^{2} + v2f^{2}

25 = 25 + v2f^{2} - 10v2f + v2f^{2}

0 = v2f^{2} - 10v2f + v2f^{2}

0 = 2v2f^{2} - 10v2f

10v2f = 2v2f^{2}

v2f = 5 m/s

v1f = 0 m/s

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