SOLUTION: Solving a science application. the height h in feet of an object after t seconds is given by the function. h= -16t^2+30t+7 how long will it take the object to hit the ground

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Question 119951: Solving a science application.
the height h in feet of an object after t seconds is given by the function.
h= -16t^2+30t+7
how long will it take the object to hit the ground? round nearest thousandth
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The object will hit the ground when h=0


h=-16t%5E2%2B30t%2B7 Start with the given equation



0=-16t%5E2%2B30t%2B7 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%2B30%2At%2B7=0 ( notice a=-16, b=30, and c=7)




t+=+%28-30+%2B-+sqrt%28+%2830%29%5E2-4%2A-16%2A7+%29%29%2F%282%2A-16%29 Plug in a=-16, b=30, and c=7



t+=+%28-30+%2B-+sqrt%28+900-4%2A-16%2A7+%29%29%2F%282%2A-16%29 Square 30 to get 900



t+=+%28-30+%2B-+sqrt%28+900%2B448+%29%29%2F%282%2A-16%29 Multiply -4%2A7%2A-16 to get 448



t+=+%28-30+%2B-+sqrt%28+1348+%29%29%2F%282%2A-16%29 Combine like terms in the radicand (everything under the square root)



t+=+%28-30+%2B-+2%2Asqrt%28337%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+=+%28-30+%2B-+2%2Asqrt%28337%29%29%2F-32 Multiply 2 and -16 to get -32

So now the expression breaks down into two parts

t+=+%28-30+%2B+2%2Asqrt%28337%29%29%2F-32 or t+=+%28-30+-+2%2Asqrt%28337%29%29%2F-32


Now break up the fraction


t=-30%2F-32%2B2%2Asqrt%28337%29%2F-32 or t=-30%2F-32-2%2Asqrt%28337%29%2F-32


Simplify


t=15+%2F+16-sqrt%28337%29%2F16 or t=15+%2F+16%2Bsqrt%28337%29%2F16


So these expressions approximate to

t=-0.209847484417864 or t=2.08484748441786


So the possible solutions are:
t=-0.209847484417864 or t=2.08484748441786


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

t=2.08484748441786


So it takes about 2.085 seconds for the object to hit the ground.