Question

Derive an expression for time to reach maximum height and hence the time of flight of a projectile

Answer 1

To find the time of flight, determine the time the projectile takes to reach maximum height. The time of flight is just double the maximum-height time.
Start with the equation:
V y =V oy + Ay t
At maximum height, V y = 0
The time to reach maximum height is t1/2= -
V oy / ay
Time of flight is t = 2t1/2 = - 2v oy/ ay
Plugging in V oy = V o sin(q) /g
Where g = 9.8m/s2
The time of flight is also determined solely by the initial velocity in the y direction and the acceleration due to gravity.