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 2000 m B 1000 m C 3000 m D 2800 m

Step-by-step solution

1. 1

   Given values

   Initial velocity $u = 280 \text{ ms}^{-1}$, angle $\theta = 30^\circ$, $g = 9.8 \text{ ms}^{-2}$, $\sin 30^\circ = 0.5$.
2. 2

   Maximum height formula

   The formula for maximum height $H$ in projectile motion is:

   $$H = \frac{u^2 \sin^2 \theta}{2g}$$
3. 3

   Substitute values

   Substitute the given values into the formula.
4. 4

   Calculate $\sin^2 \theta$

   First, calculate $\sin^2 \theta$.

   $$\sin^2 30^\circ = (0.5)^2 = 0.25$$
5. 5

   Substitute and simplify

   Substitute $u$, $\sin^2 \theta$, and $g$ into the formula.

   $$H = \frac{(280)^2 \times 0.25}{2 \times 9.8}$$
6. 6

   Calculate numerator

   Calculate the numerator.

   $$(280)^2 \times 0.25 = 78400 \times 0.25 = 19600$$
7. 7

   Calculate denominator

   Calculate the denominator.

   $$2 \times 9.8 = 19.6$$
8. 8

   Final calculation

   Divide the numerator by the denominator to get $H$.

   $$H = \frac{19600}{19.6} = 1000 \text{ m}$$