Question

During a circus act, an elderly performer thrills the crowd by catching a cannon ball shot at him. The cannon ball has a mass of\(10.0kg\)and the horizontal component of its velocity is\(8.00 m/s\)when the\(65.0kg\)performer catches it. If the performer is on nearly frictionless roller skates, what is his recoil velocity?

Short answer

The velocity of the system after collision will be \(1.07 m/s\).

Step-by-step solution

Definition of collision

According to collision theory, only a specific number of collisions between acceptable reactant particles with the correct orientation result in a detectable or noticeable change; these successful modifications are referred to as successful collisions.

Given data

The velocity of cannon ball is \({v_c} = 8.00 m/s\)in right side.

The mass of the cannon ball is\({M_c} = 10.0kg\).

The velocity of the person is\({v_p} = 0\)

The mass of the person is\({M_p} = 65kg\)

The Collison is inelastic.

Velocity of the system of players after the collision

By putting all the value into the equation we get

\(\begin{aligned}{M_c}{V_c} + {M_p}{V_p} &= + {M_T}{V_f}\\{V_f} &= \dfrac{{{M_v}{V_c} + {M_p}{V_p}}}{{{M_T}}}\\{V_f} &= \dfrac{{\left( {10} \right)\left( 8 \right) + \left( {65} \right)\left( 0 \right)}}{{\left( {10 + 65} \right)}}\\{V_f} &= 1.07\,m/s\end{aligned}\)…………………(1)

Hence the velocity of the system after collision will be\(1.07 m/s\). They will move towards right side as the velocity answer is positive.