Answer:
a) 0 seconds.
b) The stunt diver is in the air for 2.81 seconds.
Explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots
such that
, given by the following formulas:



Height of the diver after t seconds:

a) How long is the stunt diver above 15 m?
Quadratic equation with
, so the parabola is concave down, and it will be above 15m between the two roots that we found for
. So



Quadratic equation with
. Then

Negative
, which means that the stunt diver is never above 15m, so 0 seconds.
b) How long is the stunt diver in the air?
We have to find how long it takes for the diver to hit the ground, that is, t for which
. So



Quadratic equation with
. Then



Time is a positive measure, so we take 2.81.
The stunt diver is in the air for 2.81 seconds.