Question 221721
When the ball hits the ground, h=0, so set the equation equal to zero.

-16t^2 + 96t +176=0

-16(t^2 - 6t - 11)=0


What results here is a quadratic equation that cannot be factored.  You will have to use the quadratic formula or completing the square.  It turns out that completing the square is easier for this problem.


t^2 -6t -11=0
t^2 -6t +_____= 11+_____

Take HALF of the coefficient of t, which is -6 and SQUARE it.  Half of -6 would be -3, and -3 squared is +9.  Add =9 to each side:
t^2 -6t+9 = 11+9
(t-3)^2 = 20


Now you can take square root of each side like this:
{{{t-3 = 0+-sqrt(20)}}}


Then add +3 to each side:
{{{t= 3 +-sqrt(20)}}}


Reject the negative value since time cannot be negative.

{{{t= 3 +sqrt(20)}}}


Finally, either calculate this, or simplify the square root.  By approximation (my calculator is in the other room!) square root of 20 is about 4.5, so the time is about 3+4.5= 7.5 seconds--very approximately!!


The exact value is this:
{{{t= 3 + sqrt(4)*sqrt(5)}}}
{{{t= 3 + 2* sqrt(5) }}}


R^2


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamone Springs Campus