SOLUTION: The height {{{highlight(in_feet)}}} of a ball above the ground t seconds after it is thrown is h(t) = 20+32t−16t2. How long will it take for the ball to hit the ground?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The height {{{highlight(in_feet)}}} of a ball above the ground t seconds after it is thrown is h(t) = 20+32t−16t2. How long will it take for the ball to hit the ground?      Log On


   

Question 1173412: The height highlight%28in_feet%29 of a ball above the ground t seconds after it is thrown is h(t) = 20+32t−16t2. How long will it take for the ball to hit the ground?
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

To answer the problem's question, you need to solve this equation

    -16t^2 + 32t + 20 = 0


and take its larger root.


The equation is equivalent to

    4t^2 - 8t - 5 = 0


Use the quadratic formula

    t = %288+%2B-+sqrt%288%5E2+-4%2A4%2A%28-5%29%29%29%2F%282%2A4%29 = %288+%2B-+sqrt%28144%29%29%2F8 = %288+%2B-+12%29%2F8.


The larger root is  %288+%2B+12%29%2F8 = 20%2F8 = 2.5 seconds.


ANSWER.  The ball will hit the ground in 2.5 seconds.

Solved.