# Time of flight equation for projectile

The equation of the

total time of flight for a projectile is T=_{tot}2(V_{0}sinθ )/g

**Time of flight equation – derivation**

To derive the *time of flight equation* of a projectile we first have to find out the time to reach the Maximum Height by a projectile.

When the projectile reaches the maximum height then the velocity component along Y-axis i.e. V_{y} becomes 0. Say the time required to reach this maximum height is t_{max}.

The initial velocity for the motion along Y-axis (as said above) is V_{0}sinθ

Considering vertical motion along the y-axis:

V_{y} = V_{0}sinθ – g t_{max} ………………….. (1)

At the maximum height. equation 1 becomes:

_{}=> 0 = V_{0}sinθ – g t_{max}

=>t_{max}= (V_{0}sinθ )/g ……………….(2)

So this is the equation for the time required to reach the maximum height by the projectile.

**So to reach the maximum height by the projectile the time taken is (V _{0}sinθ )/g**It can be proved that the projectile takes equal time [ (V

_{0}sinθ )/g] to come back to the ground from its maximum height.

Therefore the formula of the

total time of flight for a projectile T=_{tot}2(V_{0}sinθ )/g …………………. (3)