SOLUTION: The height h in feet of an object after t seconds is given by the function h = –16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the ne

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The height h in feet of an object after t seconds is given by the function h = –16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the ne      Log On


   

Question 124287: The height h in feet of an object after t seconds is given by the function
h = –16t^2 + 30t + 3. 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!
The object will hit the ground when h=0


h+=+-16t%5E2+%2B+30t+%2B+3 Start with the given equation


0+=+-16t%5E2+%2B+30t+%2B+3 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%2B3=0 ( notice a=-16, b=30, and c=3)




t+=+%28-30+%2B-+sqrt%28+%2830%29%5E2-4%2A-16%2A3+%29%29%2F%282%2A-16%29 Plug in a=-16, b=30, and c=3



t+=+%28-30+%2B-+sqrt%28+900-4%2A-16%2A3+%29%29%2F%282%2A-16%29 Square 30 to get 900



t+=+%28-30+%2B-+sqrt%28+900%2B192+%29%29%2F%282%2A-16%29 Multiply -4%2A3%2A-16 to get 192



t+=+%28-30+%2B-+sqrt%28+1092+%29%29%2F%282%2A-16%29 Combine like terms in the radicand (everything under the square root)



t+=+%28-30+%2B-+2%2Asqrt%28273%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%28273%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%28273%29%29%2F-32 or t+=+%28-30+-+2%2Asqrt%28273%29%29%2F-32


Now break up the fraction


t=-30%2F-32%2B2%2Asqrt%28273%29%2F-32 or t=-30%2F-32-2%2Asqrt%28273%29%2F-32


Simplify


t=15+%2F+16-sqrt%28273%29%2F16 or t=15+%2F+16%2Bsqrt%28273%29%2F16


So these expressions approximate to

t=-0.095169477616144 or t=1.97016947761614


So our possible solutions are:
t=-0.095169477616144 or t=1.97016947761614


However, since a negative time doesn't make sense, our only solution is t=1.97016947761614


So the object will hit the ground at about 1.970 seconds