## Answers

Given,

mass of Ball 1, m_{1} = 4.3 kg

initial velocity of Ball 1, u_{1} = 2.0 m/s

final velocity of Ball 1, v_{1} = –6.91m/s

mass of Ball 2, m_{2} = ?

initial velocity of Ball 2, u_{2} = –5.0 m/s

final velocity of Ball 2, v_{2} = 0.11m/s

In elastic collision, law of conservation of momentum and law of conservation of energy hold.

In elastic collision, final velocities after collision, are v_{1} = [ (m_{1} – m_{2}) / (m_{1} + m_{2}) ]u_{1} + [ 2m_{2} / (m_{1} + m_{2})] u_{2}

and v_{2} = [ 2m_{1} / (m_{1} + m_{2})] u_{1} + [ (m_{2} – m_{1}) / (m_{1} + m_{2}) ]u_{2}

Let us substitute the given values in the first formula for v_{1}.

–6.91 = [(4.3 – m_{2}) / (4.3 + m_{2}) ]x2 + [ 2m_{2} / (4.3 + m_{2})]x (–5)

–6.91 = [((4.3 – m_{2})x2 – 10m_{2} ] / (4.3 + m_{2})

–6.91x (4.3 + m_{2}) = 8.6 – 2m_{2} – 10m_{2}

–29.71 – 6.91m_{2} = 8.6 – 12m_{2}

– 6.91m_{2} +12m_{2} = 8.6 + 29.71

5.09m_{2} = 38.31

m_{2} = 7.52 kg

**So, the mass of Ball 2 is 7.52 kg**