A missile is fired for maximum range with an initial velocity of `20m//s`. If `g=10m//s^(2)`, the range of the missile is

Options

A. `50m`
B. `60m`
C. `20m`
D. `40m`

Explanation

To find the range of a missile fired for maximum range with an initial velocity of \(20 \, \text{m/s}\) and \(g = 10 \, \text{m/s}^2\), we can use the formula for the range of a projectile:

### Step-by-Step Solution:

1. **Identify the formula for range**:
The range \(R\) of a projectile is given by the formula:
\[ R = \frac{v^2 \sin 2\theta}{g} \]
where \(v\) is the initial velocity, \(\theta\) is the angle of projection, and \(g\) is the acceleration due to gravity.

2. **Determine the angle for maximum range**:
The range is maximum when \(\theta = 45^\circ\). At this angle, \(\sin 2\theta = \sin 90^\circ = 1\).

3. **Substitute the values into the formula**:
Given:
- Initial velocity \(v = 20 \, \text{m/s}\)
- Acceleration due to gravity \(g = 10 \, \text{m/s}^2\)

We can substitute these values into the range formula:
\[ R = \frac{(20)^2 \cdot 1}{10} \]

4. **Calculate the range**:
\[ R = \frac{400}{10} = 40 \, \text{m} \]

5. **Final answer**:
The range of the missile is \(40 \, \text{m}\).