SOLUTION: The height h in feet of an object after t seconds is given by the function h = –16t^2 + 70t + 8. How long will it take the object to hit the ground? Round your answer to the

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Question 96024: The height h in feet of an object after t seconds is given by the function
h = –16t^2 + 70t + 8.
How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find when it hits the ground, let h=0

0+=+-16t%5E2+%2B+70t+%2B+8 Plug in h=0



Let's use the quadratic formula to solve for t:


Starting with the general quadratic

at%5E2%2Bbt%2Bc=0

the general solution using the quadratic equation is:

t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve -16%2At%5E2%2B70%2At%2B8=0 ( notice a=-16, b=70, and c=8)

t+=+%28-70+%2B-+sqrt%28+%2870%29%5E2-4%2A-16%2A8+%29%29%2F%282%2A-16%29 Plug in a=-16, b=70, and c=8



t+=+%28-70+%2B-+sqrt%28+4900-4%2A-16%2A8+%29%29%2F%282%2A-16%29 Square 70 to get 4900



t+=+%28-70+%2B-+sqrt%28+4900%2B512+%29%29%2F%282%2A-16%29 Multiply -4%2A8%2A-16 to get 512



t+=+%28-70+%2B-+sqrt%28+5412+%29%29%2F%282%2A-16%29 Combine like terms in the radicand (everything under the square root)



t+=+%28-70+%2B-+2%2Asqrt%281353%29%29%2F%282%2A-16%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



t+=+%28-70+%2B-+2%2Asqrt%281353%29%29%2F-32 Multiply 2 and -16 to get -32

So now the expression breaks down into two parts

t+=+%28-70+%2B+2%2Asqrt%281353%29%29%2F-32 or t+=+%28-70+-+2%2Asqrt%281353%29%29%2F-32


Now break up the fraction


t=-70%2F-32%2B2%2Asqrt%281353%29%2F-32 or t=-70%2F-32-2%2Asqrt%281353%29%2F-32


Simplify


t=35+%2F+16-sqrt%281353%29%2F16 or t=35+%2F+16%2Bsqrt%281353%29%2F16


So these expressions approximate to

t=-0.11144676971869 or t=4.48644676971869


So our possible solutions are:
t=-0.11144676971869 or t=4.48644676971869

However, since a negative time doesn't make sense, our only solution is

t=4.48644676971869


So it will take about 4.486 seconds to hit the ground.