diver jumps into a pool from a board ten feet above the surface of the water. Her height, h, at any time t seconds after jumping is given by the equation

Question

. What is the minimum height that she reaches? (Note: Negative values of h mean the diver is below the water.)

A.
–26 feet

B.
–10 feet

C.
–6 feet

D.
–4 feet

Answer 1

To determine the minimum height the diver reaches, we need to know the equation that describes her height $h$ as a function of time $t$. Since you didn't provide the equation, I can guide you through the general approach to finding the minimum height:

1. Identify the equation: Typically, the height $h(t)$ can be expressed as a quadratic equation of the form: $$h(t)=-a{t}^2+bt+c$$ where $a$, $b$, and $c$ are constants.

2. Find the vertex: The minimum (or maximum in this case since it is a downward-opening parabola) height occurs at the vertex of the parabola. The time at which the vertex occurs can be found using the formula: $$t_{vertex}=-\frac{b}{2a}$$

3. Substitute to find minimum height: Once you find $t_{vertex}$, substitute it back into the height equation to find the height at that time.

4. Analyse the results: If the calculated height is negative, it indicates how far below the water surface she dips.

Now, if you have the specific equation for height $h(t)$, you could provide it, and I could assist you further in calculating the minimum height. Based on your options A through D, the results will reflect the different possible minimum heights found from plugging in $t_{vertex}$ into the height equation.