Answer:
(See explanation below for further details)
Step-by-step explanation:
A. What details can you determine about the dive from the coordinates of the point (5, -8)?
First component corresponds to time and second component to depth with respect to sea level. The diver is 8 feet below sea level at 5 seconds.
B. What is the average speed of the diver in the water? How can you tell from the graph?
The average speed of the diver ([tex]\bar v[/tex]), measured in feet per second, can be calculated by the following expression:
[tex]\bar v = \frac{x_{f}-x_{o}}{t_{f}-t_{o}}[/tex]
Where:
[tex]x_{o}[/tex], [tex]x_{f}[/tex] - Initial and final depth of diver, measured in feet.
[tex]t_{o}[/tex], [tex]t_{f}[/tex] - Initial and final instant, measured in seconds.
There are three different average speeds: (i) Descent ([tex]t = 1\,s[/tex] to [tex]t = 5\,s[/tex]), (ii) Ascent ([tex]t = 5\,s[/tex] to [tex]t = 9\,s[/tex]), (iii) Descent + Ascent ([tex]t = 1\,s[/tex] to [tex]t = 9\,s[/tex])
(i) Descent ([tex]t = 1\,s[/tex] to [tex]t = 5\,s[/tex])
[tex]x_{o} = 0\,ft[/tex] and [tex]x_{f} = -8\,ft[/tex]
[tex]\bar v_{i} = \frac{-8\,ft-0\,ft}{5\,s-1\,s}[/tex]
[tex]\bar v_{i} = -2\,\frac{ft}{s}[/tex]
(ii) Ascent ([tex]t = 5\,s[/tex] to [tex]t = 9\,s[/tex])
[tex]x_{o} = -8\,ft[/tex] and [tex]x_{f} = 0\,ft[/tex]
[tex]\bar v_{ii} = \frac{0\,ft-(-8\,ft)}{9\,s-5\,s}[/tex]
[tex]\bar v_{ii} = 2\,\frac{ft}{s}[/tex]
(iii) Descent + Ascent ([tex]t = 1\,s[/tex] to [tex]t = 9\,s[/tex])
[tex]x_{o} = 0\,ft[/tex] and [tex]x_{f} = 0\,ft[/tex]
[tex]\bar v_{iii} = \frac{0\,ft-0\,ft}{9\,s-1\,s}[/tex]
[tex]\bar v_{iii} = 0\,\frac{ft}{s}[/tex]
C. Which point on the graph shows the starting location of the diver?
The initial location is when [tex]t = 0\,s[/tex], which corresponds to the intercept of the line on y-axis.
