Question

A $200\text{kg}$ cannon at rest contains a $10\text{kg}$ cannon ball. When fired, the cannon ball leaves the cannon with a speed of $90\text{m/s}$. What is the recoil speed of the cannon?

• A. $10\text{m/s}$
• B. $5\text{m/s}$
• C. $4.5\text{m/s}$
• D. $8\text{m/s}$

Answer 1

The correct option is C $4.5\text{m/s}$

Since, momentum of the system is conserved here, we have
$P_{initial}=P_{final}.....\left(i\right)$
Given, mass of cannon $m_c=200\text{kg}$
mass of cannon ball $m_b=10\text{kg}$
speed of cannon ball $v_b=90\text{m/s}$
Let recoil velocity of cannon be $v_c$
Now, from eq $\left(i\right)$ we have
$0=m_c{v}_c+m_b{v}_b\Rightarrow v_c=-\frac{m_b{v}_b}{m_c}\Rightarrow v_c=-\frac{10\times 90}{200}=-4.5\text{m/s}$
Thus, recoil speed of the cannon is $4.5\text{m/s}$.