Answer:
Chris will take 0.75 seconds to return to his starting height of 10 feet.
Step-by-step explanation:
Let the height of Chris be represented by [tex]h(t) = -16\cdot t^{2}+12\cdot t +10[/tex], where [tex]h(t)[/tex] is the height in feet and [tex]t[/tex], the time in seconds. First, we equalize the formula to a height of 10 feet and simplify the resulting expression, that is:
[tex]-16\cdot t^{2}+12\cdot t +10 = 10[/tex]
[tex]-16\cdot t^{2}+12\cdot t = 0[/tex]
Then, we simplify the expression by algebraic means:
[tex]-16\cdot t\cdot \left(t-\frac{3}{4} \right) = 0[/tex]
Roots of the polynomial are, respectively:
[tex]t = 0\,s\,\lor \,t = 0.75\,s[/tex]
First root represents the initial height of Chris, whereas the second one represents the instant when Christ returns to the same height above the surface of the water. Hence, Chris will take 0.75 seconds to return to his starting height of 10 feet.
