SOLUTION: I have tried this problem multiple times. Maybe I am overthiking it. Find the domain and range of the function that describes the height of a ball dropped from a 500-foot buildi

Question 159369This question is from textbook
: I have tried this problem multiple times. Maybe I am overthiking it.
Find the domain and range of the function that describes the height of a ball dropped from a 500-foot building.
Domain = set of values between & including 0-? seconds.
Range = height of building so it would be 500 feet, right?
forumula: h=-1/2 gs^2+v0S+h0
Now I get stuck.
Any help is appreciated.
Thanks
Jan This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the domain and range of the function that describes the height of a ball dropped from a 500-foot building.
Domain = set of values between & including 0-? seconds.
Range = height of building so it would be 500 feet, right?
forumula: h(s)=-1/2 gs^2+v0S+h0
---------------
h(s) = -(1/2)(32)s^2 + vos + ho
h(s) = -16s^2 + vos + ho
-------
If it is merely dropped, vo = 0
If the beginning height (ho) is 500 ft, ho = 500
--------
h(s) = -16s^2 + 500
When it hits the ground, h(s) = 0 ft.
-16s^2 + 500 = 0 ft
16s^2 = 500
s^2 = 500/16
s = 10sqrt(5)/4 =5.59017... seconds
-------------
Domain: 0 <= s <= 5.59017..
Range: 0 <= h <= 500
===========================
Cheers,
Stan H.
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