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

Answer:

$2.4375\ \text{m/s}$

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

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

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