Question

A man of mass $80kg$ is riding on a small cart of mass $40kg$ which is rolling along a level floor at a speed of $2m{s}^{-1}$ . He is running on the cart so that his velocity relative to the cart is $3m{s}^{-1}$ in the direction opposite to the motion of the cart. What is the speed of the centre of mass of the system

• A. $1.5m{s}^{-1}$
• B. $1m{s}^{-1}$
• C. $3m{s}^{-1}$
• D. zero

Answer 1

Answer: (D)

${\overrightarrow{v}}_{cart}={\overrightarrow{v}}_c=2\hat{i}$
$\Rightarrow {\overrightarrow{v}}_m={\overrightarrow{v}}_{mc}+{\overrightarrow{v}}_c$
$\Rightarrow {\left(\overrightarrow{v}\right)}_m=\left(-3\hat{i}\right)+2\hat{i}$
$\Rightarrow {\overrightarrow{v}}_m=\hat{i}$
Now ${\left(\overrightarrow{v}\right)}_{cm}=\frac{80\left(-\hat{i}\right)+40\left(2\hat{i}\right)}{80+40}$
${\overrightarrow{v}}_{cm}=0$