Question

At what angle should a projectile with initial velocity 'v' be thrown, so that it achieves its maximum range?

Answer 1

Step 1: Projectile motion

1. Projectile refers to an object that is in flight after being thrown or projected.
2. Projectile motion is experienced by an object that moves along a curved path under the action of gravity only.

Step 2: An illustrative diagram of projectile motion

Step 3: Solution

The range of projectiles depends on the horizontal velocity and the time in flight. The flight time depends on the vertical velocity. At $45°$ angle both horizontal and vertical velocity are equal. From the formula of range :

$\mathrm{R}=\frac{{\mathrm{u}}^2\mathrm{Sin}2\mathrm{\theta }}{\mathrm{g}}$

where, $\mathrm{R}$= range, $\mathrm{u}$= initial velocity, $\mathrm{g}$= gravitational constant.

At $\mathrm{\theta }=45°$ we will get $\mathrm{Sin}90°$ which will give us the maximum value of the range.

Hence, at $45°$angle it will achieve maximum range.