simple kinmatics

[tony873004]

A person stands on the roof of a building, 40 m high. He throws a rock directly up at 10 m/s. How long until it hits the ground?

I know how to do this in 2 steps: compute height that the rock rises to (~5 meters), then compute time for an object to free fall from 0 m/s to the ground ~45 meters below.

But isn't there a way to do it in one step?

[HallsofIvy]

You certainly should be able to get the formula for height as a function of time: you probably use it or some version of it to get the height the rock rises to.
It is h= -4.9t2+ 10t+ 40.

Now set h= 0 and solve for t (you will get two solutions- only one is positive).