Question

A large number of bullets are fired in all directions with the same speed \( v \). What is the maximum area on the ground on which these bullets will spread?

Hint:

The maximum spread area for projectiles depends on the square of their speed and is inversely proportional to the square of gravitational acceleration.

Answer 1

Step 1: Horizontal range of a projectile
The horizontal range \( R \) of a projectile is given by: \[ R = \frac{u^2 \sin 2\theta}{g} \] where \( u \) is the initial speed, \( \theta \) is the angle of projection, and \( g \) is the acceleration due to gravity. Step 2: Maximum horizontal range
The maximum horizontal range occurs when \( \sin 2\theta = 1 \), i.e., \( \theta = 45^\circ \). Then: \[ R_{\text{max}} = \frac{u^2}{g} \] Step 3: Area of spread
Assuming bullets are fired in all directions, the spread forms a circle with radius \( R_{\text{max}} \). The area \( A \) is: \[ A = \pi R_{\text{max}}^2 = \pi \left( \frac{u^2}{g} \right)^2 \]