The time of flight of a projectile is basically how long the projectile has stayed in the air. This equation is based off of the quadratic equation. It was derived from one of the 3 fundamental kinematics equations. The time of flight equation can be derived from one of the basic kinematics equation: X = Xo + VoT + ½AT² into this larger equation, which is the result if you solve for T:
The time of flight of a projectile is equal to the Y component of the initial velocity then either added, or subtracted from the square root of the Y component of the initial velocity squared minus two times the acceleration due to gravity (g) multiplied by the final height minus the initial height then all of that divided by the acceleration due to gravity. In this case, you can replace the X of the initial kinematic equation with Y, and still receive the same answer to the problem. Also, we have replaced Voy with its respective vector equation in order to make the problem simpler by using the numbers that we already know, which will make it easier when we get to the scenario to do the math involved with the problem.
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