Suppose you are standing on the ground and throwing a stone straight up in the air. Let assume, for simplicity, that the gravitational constant is 10 meters per second per second. Neglecting air resistance, the stone's distance from the ground, in meters, after t seconds will be h(t)=−5t^2+vt.
At what velocity v do you have to throw the stone so that it reaches a height of exactly 9.8 meters before it starts to fall back towards the earth?
I have tried to derivate the function, but still stands still on this.