Question

A $100\text{m}$ long train crosses a man travelling at $5\text{km/h}$ in the opposite direction in $7.2\text{s}$. Then the velocity of train is

• A. $40\text{km/h}$
• B. $25\text{km/h}$
• C. $20\text{km/h}$
• D. $45\text{km/h}$

Answer 1

The correct option is D $45\text{km/h}$

Given velocity of man $V_M=5\text{kmph}$
Let $V_T$ be velocity of train,
Velocity of train wrt man is
$\Rightarrow {\overrightarrow{V}}_{TM}={\overrightarrow{V}}_T-{\overrightarrow{V}}_m$
as $V_T,V_M$ are in opposite directions
$V_{TM}=V_T+V_M=V_T+5$

Now $t=\frac{d}{V_{TM}}=\frac{100}{V_T+5}=7.2\text{sec}$
$\Rightarrow V_T+5=\frac{100}{7.2}\text{m/s}$
$V_T+5=\frac{1000}{72}\times \frac{18}{5}\text{kmph}$
$V_T+5=50$
$V_T=45\text{kmph}$