A ball is launched into the sky at 19.6 feet per second from a 58.8 meter tall building. "
Is that a typo, or a real mixture of units?
The equation is only good if the launch speed is actually 19.6 m/s, so I'll assume that.
It will strike the ground when the ball's height = 0 m !!!
-4.9t² +19.6t + 58.8 = 0
You can always use the "quadratic formula" if you want to, but ...
This set of numbers is beloved by physics teachers everywhere. Everything divides by -4.9
t² - 4t -12 = 0
...and factorizes easily:
(t + 2)(t - 6)
So t = 6 or t = -2 Disregard the negative solution.
The ball will strike the ground at t = 6 seconds
