# What is the general equation for determining where a projectile launched from the ground will land?

##### 1 Answer

This is a repeat question. However, since a general expression is to be worked out so see details below.

Range

#### Explanation:

Let the projectile be lunched with initial velocity *x* -axis.

Distance traveled horizontally in time of flight *t* gives us the Horizontal Range

Assuming zero air friction, and noticing that there is no acceleration in the horizontal direction we obtain

To obtain time of flight

It is observed that the projectile will rise initially, attain maximum height and then fall down due to gravity.

*y* direction, the final velocity in *y* direction will be

Using the formula

Take *y* direction so it is deceleration and *g*

We obtain

Substituting value of *t* in expression (1)