If an object falls from a height of h mts, t seconds after starting the fall has traveled a distance of
s(t)=-4.9t^2 + h
A workman drops a wrench from a height of 50 meters and shouts: be careful down there!
How long should a person stay away from the path of the key? At what speed does the key touch the ground?
As an answer to the first part we have
0 = -4.9t^2 + 50 subtract 50 from both sides
-50 = -4.9 t^2 divide both sides by -4.9
50 / 4.9 = t^2 take the positive root of both sides
√(50/4.9) = t ≈ 3.2 seconds
As an answer to the second part we have
-9.8 (3.2) ≈ 31.36 m / s