# Question #ddd99

##### 1 Answer

At an angle of

#### Explanation:

When a projectile is launched at an angle, let's call it *vertical* component and a *horizontal* component.

Let's assume that the projectile is launched with an initial velocity of

**Horizontally**, the projectile is not acted upon by any force. This means that the *vertical component* of its initial velocity will remain unchanged during the motion.

This means that you can write

*total time* of flight.

**Vertically**, things are not that simple. The projectile will be acted upon by the force of gravity, which means that the *vertical component* of its initial velocity will be affected by the *gravitational accceleration*,

Since the projectile starts at ground level and ends up on ground level, its *horizontal displacement* will be equal to **zero**. THis means that you can write

Solve this equation for

The only valid solution is

Replace

To get the maxium range, you need the *maximum* value of

The easiest way to figure this out is to use the following trigonometric identity

Since the *maximum* value of the sinus function is **1**, you get

Take the *arsin* from both sides of the equation to get

Therefore,