Part A: Type of Function
The situation can be modeled using a step or piecewise function. This is because the skydiver's descent can be divided into two distinct phases:
- Free fall: Before the parachute is opened, the skydiver descends rapidly due to gravity.
- Constant speed descent: After the parachute is opened, the skydiver descends at a constant speed of 17 m/s.
The model needs to account for the initial height and the phase change once the parachute opens.
Part B: Equation that Models the Situation
First, let's establish a time variable \( t \), where \( t = 0 \) is the moment the parachute is opened.
From that point onward, the height \( y \) of the skydiver can be expressed as: \[ y(t) = 760 - 17t \] where:
- \( y(t) \) is the height above the ground in meters.
- 760 is the initial height in meters.
- 17 is the constant descent rate in meters per second.
- \( t \) is the time in seconds after the parachute is opened.
Part C: Fill Out the Table Below
We can calculate the values of \( y \) for given \( x \) (where \( x = t \)) values.
\[ \begin{array}{|c|c|} \hline x (t) & y \ \hline 0 & 760 - 17(0) = 760 \ 10 & 760 - 17(10) = 760 - 170 = 590 \ 20 & 760 - 17(20) = 760 - 340 = 420 \ 30 & 760 - 17(30) = 760 - 510 = 250 \ 40 & 760 - 17(40) = 760 - 680 = 80 \ \hline \end{array} \]
Completed Table
\[ \begin{array}{|c|c|} \hline x (t) & y (height , above , ground) \ \hline 0 & 760 \ 10 & 590 \ 20 & 420 \ 30 & 250 \ 40 & 80 \ \hline \end{array} \]
This table provides the height of the skydiver at various times after opening the parachute.
As mentioned, the descent continues until the skydiver reaches the ground (i.e., height = 0), but based on the provided speeds, this model only goes down to a height of 80 meters after 40 seconds.
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