A missile is fired for maximum range with an initial velocity of $20 ext{ m/s}$. If $g=10 ext{ m/s}^2$, th

Question

A missile is fired for maximum range with an initial velocity of $20 	ext{ m/s}$. If $g=10 	ext{ m/s}^2$, the range of the missile is:

Accepted Answer

1. **Formula:** The horizontal range $R$ of a projectile is given by $R = \frac{v_0^2 \sin 2	heta}{g}$. For the range to be maximum, the angle of projection must be $	heta = 45^\circ$, making $\sin 2	heta = 1$ .
2. **Maximum Range Formula:** The expression simplifies to $R_{	ext{max}} = \frac{v_0^2}{g}$.
3. **Calculation:** Given initial velocity $v_0 = 20 	ext{ m/s}$ and acceleration due to gravity $g = 10 	ext{ m/s}^2$:
   $$ R_{	ext{max}} = \frac{(20)^2}{10} = \frac{400}{10} = 40 	ext{ m} $$

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