# Maximum Height, Time of Flight and Horizontal Range of a Projectile

Physics

## definition

### Average Velocity of Projectile

The average velocity of a projectile between the instant it crosses one third the maximum height. It is projected with making an angle with the vertical.
There will be a pair of points for which vertical velocities at the same height are in opposite direction and therefore their average sum
It is the horizontal velocity which is uniform and hence

For a general point:
Displacement in Y-direction:

Displacement in X-direction:

Now in order to calculate average velocity:
Average Velocity =

## formula

### Range of a Projectile Motion

The horizontal distance travelled by a projectile from its initial position to the position where it passes during its fall is called the horizontal range, . It is the distance travelled during the time of flight . therefore, the range is
......(1)
Or, ......(2)
Equation 2 shows that for a given projectile velocity , is maximum when is maximum, i.e. when .
The maximum horizontal range is, therefore

## diagram

### Time of Flight of a Projectile

Let, time taken to reach maximum height
Now,
and
Since, at this point, , we have:

Or,
Therefore, time of flight because of symmetry of the parabolic path.

## diagram

### Maximum Height of a Projectile

and
The maximum height is given by:
(for )
Or,