How to determine the total time of flight for a projectile launched at an angle theta to the horizontal with an initial speed u?
- First, decompose the initial velocity (u) into x and y components using trigonometry. These are x= ucos(theta) and y=usin(theta)
- Note that the x (or horizontal) component does not change but the y component decreases as the projectile moves up because gravity.
- when the projectile is at its maximum height, its velocity is zero, so taking the first half of the flight motion and use v=u+at to find the time taken to reach maximum height.
- Then simply noticing that it takes the exact same amount of time to fall from the max height as it took to get there, we just multiply the time we found above by 2 to get the total time of flight.
