Question 1158307
<font color=black size=3>
Answer: <font color=red>Either t = 5 seconds or t = 9 seconds</font>


=========================================


Work Shown:


The equation should be 
s = -16t^2 + 224t
Note the t^2 term as the first term


Plug in s = 720. Then get everything to one side. Afterward, use the quadratic formula to solve for t.


s = -16t^2 + 224t
720 = -16t^2 + 224t
0 = -16t^2 + 224t - 720
-16t^2 + 224t - 720 = 0


Quadratic Formula: Plug in a = -16, b = 224, c = -720
{{{t = (-b+sqrt(b^2-4ac))/(2a)}}} or {{{t = (-b-sqrt(b^2-4ac))/(2a)}}}


{{{t = (-224+sqrt((224)^2-4(-16)(-720)))/(2(-16))}}} or {{{t = (-224-sqrt((224)^2-4(-16)(-720)))/(2(-16))}}}


{{{t = (-224+sqrt(4096))/(-32)}}} or {{{t = (-224-sqrt(4096))/(-32)}}}


{{{t = (-224+64)/(-32)}}} or {{{t = (-224-64)/(-32)}}}


{{{t = (-160)/(-32)}}} or {{{t = (-288)/(-32)}}}


{{{t = 5}}} or {{{t = 9}}}



We get two solutions because the ball goes up, but then comes back down again. At t = 5 seconds, the ball is going up. Then at t = 9 seconds, the ball is coming back down. At each of these time values, the height of the ball is 720 feet.

</font>