Question

A train is running at a speed of $72\text{km/hr}$. A boy runs inside the train in same direction (as that of train) with a speed of $10\text{km/hr}$ with respect to the train. Find the velocity of boy as seen from the ground.

• A. $62\text{km/hr}$ along the direction of motion of train
• B. $72\text{km/hr}$ opposite to direction of motion of train
• C. $82\text{km/hr}$ along the direction of motion of train
• D. None of these

Answer 1

The correct option is C $82\text{km/hr}$ along the direction of motion of train

Let $+vex$ axis along the direction of motion of train.
$\Rightarrow$velocity of train w.r.t ground ${\overrightarrow{v}}_{t,g}=72\hat{i}\text{km/hr}$
Velocity of boy w.r.t. train,
${\overrightarrow{v}}_{b,t}=10\hat{i}\text{km/hr}$
Velocity of boy w.r.t ground:
$\Rightarrow {\overrightarrow{v}}_{b,g}={\overrightarrow{v}}_{b,t}+{\overrightarrow{v}}_{t,g}$
Or, ${\overrightarrow{v}}_{b,g}=(10\hat{i}+72\hat{i})\text{km/hr}$
$\therefore {\overrightarrow{v}}_{b,g}=82\hat{i}\text{km/hr}$
Hence, velocity of boy w.r.t ground is $82\text{km/hr}$ along the direction of motion of train.