Question

A shell is fired from a cannon. At the instant the shell is just 3 m/s, while the barrel is swimming upwards with a constant angular velocity of 2 rad/s. The magnitude of the absolute velocity of the shell is

• A. $3\frac{m}{s}$
• B. $4\frac{m}{s}$
• C. $5\frac{m}{s}$
• D. $7\frac{m}{s}$

Answer 1

The correct option is C $5\frac{m}{s}$


$V_B=r\omega =2\times 2=4\frac{m}{s}$
$V_{sB}=\text{velocity of shell w.r.t. barrel}=3\frac{m}{s}$

As shell is in barrel, the net velocity of shell
$\Rightarrow \overrightarrow{V_s}=\overrightarrow{V_B}+\overrightarrow{V_{s_B}}$

$\Rightarrow as{\overrightarrow{V}}_{B}and\overrightarrow{V_{sB}}$ are perpendicular

$|{\overrightarrow{V}}_s|=\sqrt{(3{)}^2+(4{)}^2}=5\frac{m}{s}$