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

Answer

To solve the problem of finding 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 follow these steps:

### Step 1: Understand the formula for range
The range \(R\) of a projectile launched at an angle \(\theta\) with an initial velocity \(u\) is given by the formula:

\[ R = \frac{u^2 \sin 2\theta}{g} \]

### Step 2: Determine the angle for maximum range
To achieve maximum range, the angle \(\theta\) should be \(45^\circ\). This is because \(\sin 2\theta\) reaches its maximum value of 1 when \(2\theta = 90^\circ\) or \(\theta = 45^\circ\).

### Step 3: Substitute the values into the range formula
Now that we know the angle for maximum range, we can substitute the values into the range formula. Here, \(u = 20 \, \text{m/s}\) and \(g = 10 \, \text{m/s}^2\):

\[ R = \frac{u^2}{g} = \frac{(20)^2}{10} \]

### Step 4: Calculate the range
Calculating the above expression:

\[ R = \frac{400}{10} = 40 \, \text{m} \]

### Conclusion
Thus, the range of the missile is \(40 \, \text{m}\).

---