Question

If bullets are fired in all possible directions from same point with equal velocity of 10 m s$^{-1}$ and an angle of projection 45$^\circ$, then the area covered by the bullets on the ground nearby (acceleration due to gravity 10 m s$^{-2}$) is
Identify the correct option from the following:

• A. 628 m$^2$
• B. 314 m$^2$
• C. 157 m$^2$
• D. 79 m$^2$

Hint:

For projectiles fired in all directions, the maximum range forms a circle on the ground, with the radius equal to the range at the given angle.

Answer 1

The Correct Option is B

Step 1: Calculate the range of a bullet
Velocity $v = 10$ m/s, angle $\theta = 45^\circ$, $g = 10$ m/s$^2$. Range $R = \frac{v^2 \sin 2\theta}{g} = \frac{10^2 \sin 90^\circ}{10} = \frac{100 \cdot 1}{10} = 10$ m. Step 2: Determine the area covered
Bullets are fired in all directions at 45$^\circ$, forming a circular area on the ground with radius equal to the range $R = 10$ m. Area = $\pi R^2 = \pi \cdot 10^2 = 100\pi \approx 314$ m$^2$. Step 3: Match with options
The area 314 m$^2$ matches option (2).