Editing Projectile motion (section)

=== Time of flight or total time of the whole journey ===
The total time <var>t</var> for which the projectile remains in the air is called the time-of-flight.
:<math> y=v_0 t\sin(\theta) -\frac{1}{2} g t^2 </math>

After the flight, the projectile returns to the horizontal axis (x-axis), so <math> y=0 </math>.
:<math> v_0 t\sin(\theta) =\frac{1}{2} g t^2 </math>

:<math> v_0 \sin(\theta) = \frac{1}{2}gt </math>

:<math> t=\frac{2 v_0\sin(\theta)}{g} </math>

Note that we have neglected air resistance on the projectile.

If the starting point is at height <var>y<sub>0</sub></var> with respect to the point of impact, the time of flight is:
: <math> t = \frac{d}{v \cos\theta} = \frac{v \sin \theta + \sqrt{(v \sin \theta)^2 + 2gy_0}}{g} </math>

As above, this expression can be reduced (<var>y<sub>0</sub></var> is 0) to

: <math> t = \frac{v\sin{\theta} + \sqrt{(v\sin{\theta})^2}}{g} = \frac{2v\sin{\theta}}{g}, </math> = <math> \frac{2v\sin{(45^\circ)}}{|g|} = \frac{\sqrt{2}v}{|g|}</math>

if <var>θ</var> equals 45°.