Question

A bullet is fired from a gun at the speed of 280 ms^-1 in the direction 30° above the horizontal. The maximum height attained by the bullet is
(g = 9.8 ms^-2, sin 30° = 0.5)

• A. 3000 m
• B. 2800 m
• C. 2000 m
• D. 1000 m

Answer 1

The Correct Option is D

To solve the problem of finding the maximum height attained by the bullet, we utilize the formula for the maximum height in projectile motion. The maximum height \(H\) reached by a projectile launched at an angle \(\theta\) with initial velocity \(v_0\) is given by:

\(H = \frac{v_0^2 \sin^2 \theta}{2g}\)

Where:

• \(v_0 = 280 \, \text{ms}^{-1}\) is the initial velocity of the bullet.
• \(\theta = 30^\circ\) is the angle of projection.
• \(g = 9.8 \, \text{ms}^{-2}\) is the acceleration due to gravity.
• \(\sin 30^\circ = 0.5\).

Substitute the given values into the formula:

\(H = \frac{(280)^2 \times (0.5)^2}{2 \times 9.8}\)

Calculate step-by-step:

1. \((280)^2 = 78400\)
2. \((0.5)^2 = 0.25\)
3. Multiply the results: \(78400 \times 0.25 = 19600\)
4. Finally, divide by \(2 \times 9.8 = 19.6\) to find \(H\):
5. \(H = \frac{19600}{19.6} = 1000 \, \text{m}\)

Therefore, the maximum height attained by the bullet is 1000 meters.

This confirms that the correct answer is 1000 m.