Hi everyone. It seems I've forgotten how to solve this one. I was wondering if someone could help me remember how.

Think projectile motion, straight up/down no resistance. I point out the part I have a problem with near the end. (this is all in accordance with a book on applied mathematics.)

dinitial conditions are^{2}x/dt^{2}= -gdx/dt=v_{0}x(0) = 0

x(t) = -1/2*g*t^{2}+ v_{0}*t

The book makes says that I can solve for t to get

t=v- how?_{0}/g

and then realize the next equation without any explanation.

X- how?_{max}= v_{0}^{2}/2g

I would be very grateful for help and direction on this one. Thanks.