Projectile Math: Finding the time it takes a projectile to land if it lands at the same height

I recently had to do this on one of my projects. Imagine you have a gun that is sitting on a level surface. You know that the cannon ball will land with no difference in the height from the cannon. In other words, there was no change in y-position.


Here is a general equation to model change in y-position:

 Delta y as stated before represents the change in y-position. vi stands for the initial velocity which we are given. Theta is the angle we are given to launch the projectile, and finally "g" represents a gravitational acceleration that is constant. Gravity is arbitrary, so you can use whatever value you'd like. Earth's gravity is 9.81 m/s^2.

Our goal is to get the change in time that occurs as the projectile flies(delta t). We know everything else in the equation. Since we know that delta y is equal to zero, we can algebraically rewrite this equation to solve for delta t:

Now you can use delta t to solve for things such as horizontal distance covered, and so on.

I hope I helped someone out there!