SOLUTION: The height h in feet of an object after t seconds is given by the function: h = –16t2 + 40t + 8. How long will it take the object to hit the ground? Round your answer to the ne

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The height h in feet of an object after t seconds is given by the function: h = –16t2 + 40t + 8. How long will it take the object to hit the ground? Round your answer to the ne      Log On


   

Question 775548: The height h in feet of an object after t seconds is given by the function:
h = –16t2 + 40t + 8. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

h=-16t%5E2%2B40t%2B8

when the object hits the ground h=0
0=-16t%5E2%2B40t%2B8


-8%2A%282t%5E2-5t-1%29=0

/-8
2t%5E2-5t-1=0
Find the roots of the equation by quadratic formula
iiiii
a= 2 , b= -5 , c= -1

b^2-4ac= 25 + 8
b^2-4ac= 33
%09sqrt%28%0933%09%29=%095.74%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 5 + 5.74 )/ 4
x1= 2.69
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 5 -5.74 ) / 4
x2= -0.19
Ignore negative value
2.7 seconds


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h+=+-16t%5E2+%2B+40t+%2B+8+
When the object hits the ground,
+h+=+0+
+0+=+-16t%5E2+%2B+40t+%2B+8+
+-2t%5E2+%2B+5t+%2B+1+=+0+
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-2+
+b+=+5+
+c+=+1+
+t+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A%28-2%29%2A1+%29%29+%2F+%282%2A%28-2%29%29+
+t+=+%28-5+%2B-+sqrt%28+25+%2B+8+%29%29+%2F+%28+-4+%29+
+t+=+%28-5+%2B-+sqrt%28+33+%29%29+%2F+%28+-4+%29+
+t+=+%28+-5+-+5.745+%29+%2F+%28-4%29+
Note that I had to use the (-) square root to avoid
getting negative time
+t+=+-10.745+%2F+%28-4%29+
+t+=+2.686+
The object will hit
the ground in 2.686 sec
check answer:
+-2t%5E2+%2B+5t+%2B+1+=+0+
+-2%2A+2.686%5E2+%2B+5%2A2.686+%2B+1+=+0+
+-2%2A7.215+%2B+13.43+%2B+1+=+0+
+-14.43+%2B+13.43+%2B+1+=+0+
+-14.43+%2B+14.43+=+0+
OK