# Calculus and projectile motion

## Main Question or Discussion Point

Ok.
So I need two questions answered so i can check answers with what u guys got.

1. a. On Earth, you could easily shoot a paper clip 64 feet straight up into the air with a rubber band. After t seconds, the clip will be H(t)= 64t-16t^2 feet above you.

How long will it take the clip to reach its maximum height?

b. On the moon, an identical launch would send the clip to a height of H(t)=64t-2.6t^2

How long would it take for the clip to reach its maximum height and what would be that height?

Ok. So if you could show me how you did it also it would really help.

The t value of the maximum will be a zero of H'(t) since that is when the paper clip stops going up and starts to go back down. Since H'(t) = 64-32t, 64-32t=0 => 64=32t => t=2 with H(2) = 64.

Also, you would be shooting the paperclip up at 64 feet per second from a height of 0 feet with that equation, not necessarily up 64 feet in the air.

Ok. So if you could show me how you did it also it would really help.
Can you show us how you did it?

HallsofIvy