SOLUTION: I am having problems with this word problem. The height h in feet of an object after t seconds is given by the function h=-16t^2+60t+9 How long will it take the object to hi

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Question 92924: I am having problems with this word problem.
The height h in feet of an object after t seconds is given by the function
h=-16t^2+60t+9
How long will it take the object to hit the ground. Round to the nearest thousandth.
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
When the object will reach ground, then h = 0.
So -16t%5E2+%2B+60t+%2B+9+=+0
16t%5E2+-+60t+-+9+=+0

Comparing with the standard form ax%5E2+%2B+bx+%2B+c+=+0, here a = 16, b = -60, c = -9.
From Sreedharacharya's formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%28-%28-60%29+%2B-+sqrt%28+%28-60%29%5E2-4%2A16%2A%28-9%29+%29%29%2F%282%2A16%29+ [substituting the values of a, ,b & c]
t+=+%2860+%2B-+sqrt%28+3600%2B576+%29%29%2F32+
t+=+%2860+%2B-+64.622%29%2F32+
t+=+3.894 or t+=+-0.145

But t is time and hence cannot be negative.
So the object will reach ground after t+=+3.894 seconds.