A train of $150 \mathrm{m}$ length is going towards north direction at a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. A parrot flies at a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$ towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to

• A

  $12 \mathrm{s}$
• B

  $8 \mathrm{s}$
• C

  $15 \mathrm{s}$
• Correct answer
  D

  $10 \mathrm{s}$

Solution

The relative velocity of the bird with respect to the train is :

$\Rightarrow {\overrightarrow{V}}_{\mathrm{BT}}={\overrightarrow{V}}_{\mathrm{B}}-{\overrightarrow{V}}_{\mathrm{T}}$
$\left|V_{\mathrm{BT}}\right|=5-\left(-10\right)=15 \mathrm{m} {\mathrm{s}}^{-1}$
[because they are going in the opposite direction]



$\therefore$ time taken by the bird to cross the train $=\frac{150}{15}=1\mathrm{0 } \text{s}$

Hence, the correct answer is option: 'D'.