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 39.0 kg and its horizontal component of velocity is 6.50 m/s just before the 65.0 kg performer catches it. If the performer is initially motionless on nearly frictionless roller skates, what is his speed immediately after catching the cannon ball

Answer 1

`2.4375\ \text{m/s}`

Step-by-step explanation:

`m_1` = Mass of cannon ball = 39 kg

`m_2` = Mass of performer = 65 kg

`u_1` = Initial horizontal component of cannon ball's velocity = 6.5 m/s

`u_2` = Initial horizontal component of performer's velocity = 0

v = Velocity of combined mass

As the momentum of the system is conserved we have

`m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow v=(m_1u_1+m_2u_2)/(m_1+m_2)\\\Rightarrow v=(39* 6.5+0)/(39+65)\\\Rightarrow v=2.4375\ \text{m/s}`

The speed of the performer immediately after catching the cannon ball is
`2.4375\ \text{m/s}`.