Question

A swimmer dives into a lake and swims to the surface in a parabolic path. path of the swimmer can be modeled by the equation

h (t) = t - 4t-where h is the height in
feet, and t is the time in seconds.
Complete the statement.
The diver will reach the surface of the water
after seconds.

Answer 1

the diver will reach the surface of the water after 1/4 seconds.

Explanation:

To find when the swimmer reaches the surface of the water, we need to set h(t) to zero since the surface of the water is at a height of zero feet.

0 = t - 4t^2

Simplifying the equation, we get:

4t^2 = t

4t^2 - t = 0

t(4t - 1) = 0

So, either t = 0 (which corresponds to the initial time when the swimmer is at the surface) or 4t - 1 = 0. Solving for t, we get:

4t - 1 = 0

4t = 1

t = 1/4

Therefore, the diver will reach the surface of the water after 1/4 seconds.