One day I decide I want to see how high I can throw a rock. I throw a rock straight up in the air and it has a speed of 30 m/s when it leaves my hand. I then realize this was foolish, as I need to get out of the way before the rock comes back down and hits me on the head. How many seconds do I have to move out of the way after I throw the rock?

Question

Details and assumptions
The acceleration of gravity is −9.8 m/s^2.
Treat me as a point mass.

Answer 1

Upward motion:
h=v₀t-gt²/2
v= v₀-gt
v=0 => t=v₀/g
h= v²/2g =30²/2•9.8=45.9 m
t=sqrt{2h/g} =sqrt{2•45.9/9.8} = 3.06 s.
t(total)=2•t = 2•3.06 =6.12 s.