Question

Two bombs $A$ and $B$ are projected in air. $A$ is thrown with a speed of $30\text{m/s}$ and $B$ with a speed of $40\text{m/s}$ as shown in the figure. What is the separation between them after $t\text{s}$ ?

• A. $70t\text{m}$
• B. $50t\text{m}$
• C. $10t\text{m}$
• D. $20t\text{m}$

Answer 1

The correct option is B $50t\text{m}$

Taking the reference axis for bomb as shown in figure, the acceleration of bombs is given as,
${\overrightarrow{a}}_A=-g{\text{m/s}}^2\hat{j}$
${\overrightarrow{a}}_B=-g{\text{m/s}}^2\hat{j}$
hence relative acceleration between bombs given as,
$\Rightarrow$acceleration of $A$ w.r.t $B$
${\overrightarrow{a}}_{AB}={\overrightarrow{a}}_A-{\overrightarrow{a}}_B=0$
Similarly,
velocity of $A$ w.r.t $B$ is,
${\overrightarrow{v}}_{AB}={\overrightarrow{v}}_A-{\overrightarrow{v}}_B$
From the figure we can see that angle between ${\overrightarrow{v}}_A\&{\overrightarrow{v}}_B$ is ${90}^{\circ }$
$\therefore |{\overrightarrow{v}}_{AB}|=\sqrt{{30}^2+{40}^2}=50\text{m/s}$
Separation between the bombs after $t=1\text{s}$ is:
$S=|{\overrightarrow{v}}_{AB}|\times t$
$\therefore S=50\times t=50t\text{m}$
Where $S$ is the relative distance between bombs or separation between them.