Question

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is _______ m/s. (take g = 10 m/s\(^2\))

Answer 1

Correct Answer: 8

Step 1: Understanding the Concept:
When a projectile is fired with a fixed speed, its horizontal range depends on the angle of projection. The maximum possible range is achieved when the angle of projection is $45^\circ$.
Step 2: Key Formula or Approach:
Horizontal range formula: $R = \frac{u^2 \sin(2\theta)}{g}$
For maximum range, $\theta = 45^\circ \implies \sin(90^\circ) = 1$.
Maximum range: $R_{max} = \frac{u^2}{g}$
Step 3: Detailed Explanation:
We are given that the farthest distance (maximum range) the bullets can reach is $R_{max} = 6.4 \text{ m}$.
The acceleration due to gravity is $g = 10 \text{ m/s}^2$.
Substitute these values into the maximum range formula:
\[ R_{max} = \frac{u^2}{g} \] \[ 6.4 = \frac{u^2}{10} \] Multiply both sides by 10:
\[ u^2 = 6.4 \times 10 = 64 \] Take the square root to find the initial speed $u$:
\[ u = \sqrt{64} = 8 \text{ m/s} \] Step 4: Final Answer:
The speed of the bullets is 8 m/s.