Anti-gravity Project Estimation

Understanding the equations

Let’s use the kinematics equation to estimate the time-of-flight of an object between the time you toss it up from a height h₀ (0<h₀<1m) and when it hits the floor after reaching the highest point h_max <2.75m.

For a linear motion with constant acceleration (deceleration in our case) the traveled distance and speed given the initial speed v₀ and a=-g are

At the highest point v=0, so the time it takes the object to reach h_max is t=v₀/g, and so h_max=h₀+v₀²/(2g) (3). When the object starts to fall down, its initial speed is zero and now a=g, so the time it takes the object to hit the floor is given by:

h₀ + v₀²/(2g) = gt²/2

And so the total time-of-flight is given by

From equation (3) we could also derive the restriction on v₀:

As a consequence, if you toss it up right from the floor level, i.e. h₀=0m, then the maximum initial speed could be v₀=7.35 m/s. Then the max time of flight is t=1.5s. The exploration of the different possible values for v₀ given h₀ are a task suitable for LabView.

Notice that the project requires a minimum time of 4s! Here we’ve been talking about objects with gravity as the only main external force acting on it, i.e. object with small surfaces such that the air (yes, there’s air around us!) doesn’t play any important role. Air can help to bring the max time of flight to above 4s, actually up to 20s according to the current record we know of.