Question

Suppose a diver jumps from a ledge that is 115 feet above the ocean and the initial upward velocity is 8 feet per second. The vertical motion of the diver can be modeled by the function h = −t^2 + 8t + 115. How long will it take until the diver enters the water? How do you know?

Answer 1

The given function of the height of the diver is

`h=-t^2+8t+115`

h is the height in feet

t is the time in seconds

To find the time for the whole motion equate h by 0, as when the diver inter the water his jumper height will be zero. (The surface of the water is the initial position)

`0=-t^2+8t+115`

Switch the 2 sides and change all signs to opposite

`t^2-8t-115=0`

Now, we have a quadratic equation, then we will use the calculator to find the values of t

`\begin{gathered} t=15.44552314 \\ \\ t=-7.445523142 \end{gathered}`

Since time can NOT be a negative value, then we will ignore the 2nd value of t

The answer should be about 15.44 seconds to the nearest 2 decimal place