Question

In the figure shown, the two projectiles are fired simultaneously, The minimum distance between them during their flight is

• A. $20m$
• B. $10\sqrt{3}m$
• C. $10m$
• D. None of these

Answer 1

Answer: (B)

$10\sqrt{3}m$

We would study the relative motion of the left projectile with respect to the right projectile.

Relative velocity in x-axis=$v_x=20\sqrt{3}\cos {60}^{\circ }+20\cos {30}^{\circ }=20\sqrt{3}m/s$

Relative velocity in y-axis=$v_y=20\sqrt{3}\sin {60}^{\circ }-20\sin {30}^{\circ }=20m/s$

$tani=\frac{v_y}{v_x}=1/\sqrt{3}$

Now d is the minimum separation between the projectiles.

$d=D\sin i=20\sqrt{3}\times \frac{1}{2}=10\sqrt{3}m$