On which factors does the value of the range of a projectile depend? On which factors does the maximum value of the range depend?

(N/A) The horizontal range $R$ of a projectile launched with initial velocity $u$ at an angle $\theta$ with the horizontal is given by the formula: $R = \frac{u^2 \sin(2\theta)}{g}$.
$1$. The value of the range $R$ depends on:
- The initial velocity $(u)$: $R$ is directly proportional to the square of the initial velocity $(u^2)$.
- The angle of projection $(\theta)$: $R$ depends on the sine of twice the angle of projection $(\sin(2\theta))$.
- The acceleration due to gravity $(g)$: $R$ is inversely proportional to the acceleration due to gravity $(g)$.
$2$. The maximum value of the range $(R_{max})$ depends on:
- The initial velocity $(u)$: $R_{max} = \frac{u^2}{g}$. Thus,it depends on the square of the initial velocity $(u^2)$.
- The acceleration due to gravity $(g)$: $R_{max}$ is inversely proportional to $g$.