QUADRATIC MODELS! (need to figure this out before Friday!) HELP!

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A catapult fires a boulder from ground level with initial vertical velocity 160 ft/s.

a) Give a function for the height 's', of the boulder in terms of the time 't', that has passed since it was fired.

b) How long would it take for the boulder to reach its maximum height?

c) Would it be possible for a boulder fired from this catapult to pass over a hill 300 ft high, and hit the castle on the other side? Explain to me this one because it's confusing me =[

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Someone help me! I tried to do this but I just keep getting myself confused.

EDIT: It is okay if you partially understand the problem, any ideas are acceptable. I just need some ideas on how to begin on the "right road". Thank you again!

QUADRATIC MODELS! (need to figure this out before Friday!) HELP!

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A catapult fires a boulder from ground level with initial vertical velocity 160 ft/s.

a) Give a function for the height 's', of the boulder in terms of the time 't', that has passed since it was fired.
The general formula is,
$\displaystyle s=-\frac{1}{2}gt^2+v_0 t+s_0$
Thus,
$\displaystyle s_0=0$ And,
$\displaystyle v_0=+160$
The decelleration is,
$\displaystyle g=32$ feet per second per second.
Thus,
$\displaystyle s=-16t^2+160t$
b) How long would it take for the boulder to reach its maximum height?
Make height is when velocity is null.
The velocity equation is the derivative of this,
$\displaystyle v=-32t+160$
Make it zero and solve,
$\displaystyle t=5$ seconds.
c) Would it be possible for a boulder fired from this catapult to pass over a hill 300 ft high, and hit the castle on the other side? Explain to me this one because it's confusing me =[
After 5 seconds it reaches maximum height.
Which is,
$\displaystyle h(5)$. Evaluate the height at five and see whether it exceedes 300 or not.