Question

A gun mounted on a car moving at a speed of $25\text{m/s}$ fires at an angle of ${60}^{\circ }$ with the horizontal and a velocity of $200\text{m/s}$ relative to the gun in the direction of motion of the car. Find the distance between the gun and the bullet when the bullet hits the ground.

• A. $2000\text{m}$
• B. $2500\text{m}$
• C. $2000\sqrt{3}\text{m}$
• D. $500\sqrt{3}\text{m}$

Answer 1

The correct option is C $2000\sqrt{3}\text{m}$

As we know distance between any two point is independent of frame of reference.Therefore solving this question in frame of car.

Horizontal component of velocity of bullet w.r.t car; $v_x=200\cos {60}^{\circ }\text{m/s}=100\text{m/s}$
Vertical component of velocity of bullet w.r.t car; $v_y=200\sin {60}^{\circ }\text{m/s}=100\sqrt{3}\text{m/s}$

Time of flight;$t=\frac{2v_y}{g}=\frac{2\times 100\sqrt{3}}{10}=20\sqrt{3}\text{s}$

Distance covered by the bullet in time$t=v_x\times t=100\times 20\sqrt{3}\text{m}=2000\sqrt{3}\text{m}$

$\text{Distance between the gun and the bullet}=\text{Distance covered by the bullet in time}t\text{in car frame}=2000\sqrt{3}\text{m}$