a rock is thrown from the top of a tal building the height i

a rock is thrown from the top of a tal building the height in feet of the rock above the ground after t sec is given the formula h(t)=-16t^2-8t+529. After how many seconds will the rock reach a height of 200 feet above the ground

Solution

h(t)=-16t^2-8t+529

After how many seconds will the rock reach a height of 200 feet above the ground?

h(t) = 200

200 = -16t^2 -8t +529

-16t^2 - 8t +329 =0

solve the quadratic equation using formula for root:

x = (-b +/- sqrt(b^2 -4ac) )/2a

-16t^2 - 8t +329 =0

t = ( - b+- sqrt(b^2 - 4ac) )/2a

= ( 8 +/- sqrt(8^2 +4*16*329) )/-32

= - 4.79 , 4.29

Negelect -ve root.

So, it takes 4.29 seconds to reach a height of 200 feet