SOLUTION: The height h in feet of an object after t seconds is given by the function h = –16t^2 + 40t + 10. How long will it take the object to hit the ground? Round your answer to th

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Question 103591: The height h in feet of an object after t seconds is given by the function
h = –16t^2 + 40t + 10.
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 the object will hit the ground, let h=0 and solve for t

0=-16t%5E2+%2B+40t+%2B+10
Solved by pluggable solver: Quadratic Formula
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%2B40%2At%2B10=0 ( notice a=-16, b=40, and c=10)





t+=+%28-40+%2B-+sqrt%28+%2840%29%5E2-4%2A-16%2A10+%29%29%2F%282%2A-16%29 Plug in a=-16, b=40, and c=10




t+=+%28-40+%2B-+sqrt%28+1600-4%2A-16%2A10+%29%29%2F%282%2A-16%29 Square 40 to get 1600




t+=+%28-40+%2B-+sqrt%28+1600%2B640+%29%29%2F%282%2A-16%29 Multiply -4%2A10%2A-16 to get 640




t+=+%28-40+%2B-+sqrt%28+2240+%29%29%2F%282%2A-16%29 Combine like terms in the radicand (everything under the square root)




t+=+%28-40+%2B-+8%2Asqrt%2835%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+=+%28-40+%2B-+8%2Asqrt%2835%29%29%2F-32 Multiply 2 and -16 to get -32


So now the expression breaks down into two parts


t+=+%28-40+%2B+8%2Asqrt%2835%29%29%2F-32 or t+=+%28-40+-+8%2Asqrt%2835%29%29%2F-32



Now break up the fraction



t=-40%2F-32%2B8%2Asqrt%2835%29%2F-32 or t=-40%2F-32-8%2Asqrt%2835%29%2F-32



Simplify



t=5%2F4-sqrt%2835%29%2F4 or t=5%2F4%2Bsqrt%2835%29%2F4



So the solutions are:

t=5%2F4-sqrt%2835%29%2F4 or t=5%2F4%2Bsqrt%2835%29%2F4






Since a negative time doesn't make any sense, the only solution is approximately

t=2.729


So it will take about 2.729 seconds for the object to hit the ground