Vertical motion

height versus time for the solid metal ball

The vertical height in metres versus the instant of time in seconds after launching (at t=0) the solid metal ball with an initial upward speed of v0=20 m/s.

For the height as a function of time of a vertically moving solid metal ball close to the surface of earth we have learned in secondary school the expression

y(t) = v₀t - gt²/2

The instant t that the metal ball returns to its starting point y=0 can be calculated from

0 = v₀t - gt²/2 = (v₀ - gt/2)t

which has two solutions:

t = 0     and     t = 2v₀/g