Question with gravity, speed, heights

[SOLVED] question with gravity, speed, heights

1. The problem statement, all variables and given/known data
a boy fires a 60g pebble with his slingshot. the pebble leaves the slingshot at 35m/s.
a) how high above the slingshot will the pebble rise if it is fired straight up?
b) if the pebble is fired so that it goes in an arc and has a speed of 10m/s at its maximum height, what will the maximum height be?
c) at what speed would an 80g pebble have to be fired to reach the same height as the pebble in (a)? Assume that the 80g pebble is also fired straight up.


2. Relevant equations
I'm just going to guess some relevant equations, because I'm so lost.
d = vt
F = mg
Eg = mg[tex]\Delta[/tex]h


3. The attempt at a solution
I tried basic multiplication, division, and other stuff... couldn't figure it out

You're help is greatly appreciated. Thanks a lot

EDIT: I just looked at the teacher's solution that she wrote, and it was mgh = [tex]\frac{mv_{1}^{2}}{2}[/tex], but how did she arrive at that? Thanks
Also, from that equation it gets narrowed down to h = [tex]\frac{v_1^2}{2g}[/tex]

 

Sorry, you're right... it should be divided by 2... I'll fix it right now. But, with the correct solution now, how did she arrive at that?

 

Kinetic Energy = 1/2mv[tex]^2[/tex]
Gravitational Energy (Eg) = mg[tex]\Delta[/tex]h