Aball is thrown from a height of
123
feet with an initial downward velocity of
11/fts
. the ball's height
h
(in feet) after
t
seconds is given by the following.
=h−123−11t16t2
how long after the ball is thrown does it hit the ground?

Define
g = 9.8 32.2 ft/s², the acceleration due to gravity.

Refer to the diagram shown below.
The initial height at 123 feet above ground is the reference position. Therefore the ground is at a height of - 123 ft, measured upward.

Because the initial upward velocity is - 11 ft/s, the height at time t seconds is
h(t) = -11t - (1/2)gt²
or
h(t) = -11t - 16.1t²

When the ball hits the ground, h = -123.
Therefore
-11t - 16.1t² = -123
11t + 16.1t² = 123
16.1t² + 11t - 123 = 0
t² + 0.6832t - 7.64 = 0

Solve with the quadratic formula.
t = (1/2) [-0.6832 +/- √(0.4668 + 30.56) ] = 2.4435 or -3.1267 s
Reject the negative answer.

The ball strikes the ground after 2.44 seconds.

2.44 s