Question

A car of mass 500 kg (including the mass of a block) is moving on a smooth road with velocity $1.0m{s}^{-1}$ along positive x-axis. Now a block of mass 25 kg is thrown outside with absolute velocity of $20m{s}^{-1}$ along positive z-axis. The new velocity of the car is $\left(m{s}^{-1}\right)$.

• A. $10\hat{i}+20\hat{k}$
• B. $10\hat{i}-20\hat{k}$
• C. $\frac{20}{19}\hat{i}-\frac{20}{19}\hat{k}$
• D. $10\hat{i}-\frac{20}{19}\hat{k}$

Answer 1

Answer: (C)

$\frac{20}{19}\hat{i}-\frac{20}{19}\hat{k}$

Initial and Final momentum of the system has to be same .
${\overrightarrow{P}}_i={\overrightarrow{P}}_f$

$\therefore \left(500\right)\left(\hat{i}\right)=\left(25\right)\left(20\hat{k}\right)+475\overrightarrow{v}$

$\therefore \overrightarrow{v}=\left[\right(\frac{20}{19}\hat{i})-(\frac{20}{19}\hat{k}\left)\right]m/s$