If an egg is thrown up and off the roof of a 100 foot building with an initial upward velocity of 10 feet per second, how long until it hits the ground?

The equation of the height as a function of time for this case is given by:

h (t) = - 16t ^ 2 + 10t + 100

By the time the egg hits the ground we have:

-16t ^ 2 + 10t + 100 = 0

We look for the roots of the polynomial:

t1 = - 2.2069555463432966

t2 = 2.8319555463432966

As it is about time, we use the positive root:

t = 2.83 s

Answer:

it hits the ground at:

t = 2.83 s