A train of length $L$ move with a constant speed $V_t.$ A person at the back of the train fires a bullet at time $t=0$ towards a target which is at a distance of $D$ (at time $t=0$ ) from the front of the train (on the same direction of motion). Another person at the front of the train fires another bullet at time $t=T$ towards the same target. Both bullets reach the target at the same time. Assuming the speed of the bullets $V_b$ are same, the length of the train is

• A

  $T\left(V_b\times 2V_t\right)$
• Correct answer
  B

  $T\left(V_b+V_t\right)$
• C

  $2T\left(V_b+2V_t\right)$
• D

  $2T\left(V_b-2V_t\right)$

Solution

Bullets from both person reaches target at same instant, so we equate time to get,

$\frac{L+D}{\left(v_t+v_b\right)}=\frac{D}{\left(v_b+v_t\right)}+T$

$L=\left(v_b+v_t\right)T$

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