Question 1162272
A toy rocket launched vertically into the air has position function 
{{{s(t) = 96*sqrt(t) - 12t^2}}} , where s = 0 is the ground, s is measured in meters and t > 0 is measured in seconds.
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Strange function, but OK.
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(a) How many seconds does the rocket spend traveling upward?
Apx 1.587 seconds
Verify the function if you want an algebraic solution.
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(b) After how many seconds does the rocket return to the ground?
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{{{s(t) = 96*sqrt(t) - 12t^2}}} 
At s(t) = 0:
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{{{s(t) = 96*sqrt(t) - 12t^2 = 0}}}
{{{96*sqrt(t) = 12t^2}}}
{{{8*sqrt(t) = t^2}}}
64t = t^4
t = 4 seconds
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(c) What is the maximum height reached by the rocket?
Apx 90.712 meters
Verify the function if you want an algebraic solution.