SOLUTION: An object dropped from a height of 600 feet has a height h(t) after t seconds given by h(t) = 600 − 16t². Express t as a function of height h and find the time it takes to reach

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Question 1175266: An object dropped from a height of 600 feet has a height h(t) after t seconds given by h(t) = 600 − 16t². Express t as a function of height h and find the time it takes to reach a height of 400 feet. Be sure to include a graph of h(t) and your new function, and use this graph to explain how you know your answer is correct. You may use graphing calculator to make this graph.
I really need a more detailed explanation in words too, I'd really appreciate this!!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An object dropped from a height of 600 feet has a height h(t) after t seconds given by h(t) = 600 − 16t².
Express t as a function of height h and find the time it takes to reach a height of 400 feet.
h = 600 - 16t^2
16t^2 = 600 - h
divide eq by 16
t^2 = 37.5 - h%2F16
Find square root of both sides
t = sqrt%2837.5+-%28h%2F16%29%29
find t when h=400
t = sqrt%2837.5+-%28400%2F16%29%29
t = sqrt%2837.5+-+25%29
t = sqrt%2812.5%29
t = 3.535 sec to reach a height of 400 ft
:
Be sure to include a graph of h(t) and your new function,
graph of f(x) = 600-16x^2, green line is 400ft right above the 3.5 sec
+graph%28+300%2C+200%2C+-8%2C+8%2C+-200%2C+700%2C+600-16x%5E2%2C+400%29+
graph of new function t(x) = sqrt%2837.5-%28x%2F16%29%29
+graph%28+300%2C+200%2C+-100%2C+700%2C+-6%2C+10%2C+sqrt%2837.5-%28x%2F16%29%29%2C+3.5%29+
green line is 3.5 sec right above 400 ft
and use this graph to explain how you know your answer is correct.