6 sec can take penny to strike the ground.
Solution:
Given data:
[tex]H_0=288[/tex] feet
[tex]V_0=48[/tex] feet
[tex]h(t)=288+48t-16t^2[/tex]
Re-arrange the terms from greatest degree to smallest degree.
[tex]h(t)=-16t^2+48t+288[/tex]
We can solve it by applying quadratic formula,
[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a = –16, b = 48, c = 288
[tex]$t=\frac{-48\pm \sqrt{48^2-4(-16)(288)}}{2(-16)}[/tex]
[tex]$t=\frac{-48\pm \sqrt{2304+18432}}{-32}[/tex]
[tex]$t=\frac{-48\pm \sqrt{20736}}{-32}[/tex]
[tex]$t=\frac{-48\pm144}{-32}[/tex]
Now, write find two t's using plus and minus operation.
[tex]$t=\frac{-48+144}{-32},\ \ t=\frac{-48-144}{-32}[/tex]
[tex]$t=\frac{96}{-32},\ \ t=\frac{-192}{-32}[/tex]
t = –3 (or) t = 6
We cannot write time is negative. so neglect t = –3.
Therefore t = 6.
Hence 6 sec can take penny to strike the ground.
