# Time of Flight

## Time of Flight

Let a particle is projected with velocity u at angle θ with the horizontal. We can write the x and y components of the initial velocity as ux = u cosθ, uy = u sinθ. The acceleration of the particle in x and y direction is ax = 0 and ay = – g.

What is Time of Flight?

The total time taken by the projectile to go up and come down to the same level from which it was projected is called time of flight.

For vertical upward motion, using vy = uy + ayt.

We get, vy = uy + ayt and ay = -g

Hence, 0 = uy + ayt = u sinθ – gt

$$t=\frac{{{u}_{y}}}{g}=\frac{u\sin \theta }{g}$$,

Now as the time taken to go up is equal to the time taken to come down, so time of flight is:

$$Time\,\,of\,\,flight\left( T \right)=2t=\frac{2{{u}_{y}}}{g}=\frac{2u\sin \theta }{g}$$,

∴ $$Time\,\,of\,\,flight\left( T \right)=\frac{2u\sin \theta }{g}$$.

Where,

T = Time of Flight (sec),

u = Initial Velocity (m/ sec),

θ = Angle of the initial velocity from the horizontal plane (radians/ degrees),

g = Acceleration due to gravity (9.8 m/ sec²).