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Time of flight equation for projectile

The equation of the total time of flight for a projectile is Ttot = 2(V0sinθ )/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.

how to calculate the Time to reach the Maximum Height by a projectile
projectile motion: components of initial velocity V0

When the projectile reaches the maximum height then the velocity component along Y-axis i.e. Vy becomes 0. Say the time required to reach this maximum height is tmax.
The initial velocity for the motion along Y-axis (as said above) is V0sinθ

Considering vertical motion along the y-axis:

Vy = V0sinθ  – g tmax ………………….. (1)

At the maximum height. equation 1 becomes:
=> 0 = V0sinθ  – g tmax

=> tmax= (V0sinθ )/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  (V0sinθ )/g

It can be proved that the projectile takes equal time [ (V0sinθ )/g] to come back to the ground from its maximum height.

Therefore the formula of the total time of flight for a projectile Ttot = 2(V0sinθ )/g …………………. (3)

See also  A ball thrown vertically upward reaches a certain height and comes down again. What can you say about its kinetic energy at the maximum height?
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