Projectiles

Calculations for Vertical Movement

In order for a body (in this case the projectile) to move vertically upwards an
initial speed Vov is required.

On its way up the body is affected by the gravitational acceleration g, which will
brake the body.

The air resistance will act in the same direction as g (deceleration).
When the final velocity Vv equals 0, the body has reached its final height h, and
then the vertical downward movement will immediately begin with the initial speed
= 0.
On its way down the body is affected by g, which will increase the speed.
The air resistance will act in the opposite direction of g (deceleration).
Final speed is reached when the body is at the same height from which it started.
As the air resistance is difficult to calculate (depends on air pressure, humidity,
body shape, speed and surface) it has not been included in the calculations for
projectile throwing.

Calculations for Projectile Throwing

When a projectile is thrown, it will always be under some angle to the horizontal
(45 degrees will - everything else being equal - give the longest throw).
The initial speed Vo will be subject to direction, and it dissolves in two
composants:
Vov = vertically, Voh = horizontally (trigonometry).

Firstly, we calculate what happens in vertical direction. Time is calculated for the
upward movement. Time is calculated for the downward movement (with no air
resistance the two are equal).
The total time of movement upwards and downwards equals the sum of the two
times.

Secondly, we calculate what happens in horizontal direction.
Ignoring any air resistance the velocity in horizontal direction is constant, and the
total horizontal distance L_total can be found as product of Voh and total time.

Example: