Question

A ball is fired at 4 m/s to the right and bounces off a second ball, initially at rest, and comes back to the left at 2m/s. What is the velocity of the second ball? Assume both balls have a mass of 3.93kg and make to the right positive

Answer 1

Given data

*The given mass of the first ball is m = 3.93 kg

*The mass of the second ball is M = 3.93 kg

*The initial velocity of the first ball is u_1 = 4 m/s

*The initial velocity of the second ball is u_2 = 0 m/s

*The final velocity of the first ball is v_1 = -2.0 m/s

The formula for the velocity of the second ball is given by the conservation of momentum as

`\begin{gathered} p_i=p_f \\ mu_1+Mu_2=mv_1+Mv_2 \end{gathered}`

Substitute the known values in the above expression as

`\begin{gathered} 3.93*4+3.93*0=3.93*-2.0+3.93* v_2 \\ 15.72=-7.86+3.93v_2 \\ v_2=6\text{ m/s} \end{gathered}`

Hence, the final velocity of the second ball is v_2 = 6 m/s