Question

What details can you determine about the dive from the coordinates of the point (5, −8)?

Answer 1

(See explanation below for further details)

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 (
`\bar v`), measured in feet per second, can be calculated by the following expression:

`\bar v = (x_(f)-x_(o))/(t_(f)-t_(o))`

Where:

`x_(o)`,
`x_(f)` - Initial and final depth of diver, measured in feet.

`t_(o)`,
`t_(f)` - Initial and final instant, measured in seconds.

There are three different average speeds: (i) Descent (
`t = 1\,s` to
`t = 5\,s`), (ii) Ascent (
`t = 5\,s` to
`t = 9\,s`), (iii) Descent + Ascent (
`t = 1\,s` to
`t = 9\,s`)

(i) Descent (
`t = 1\,s` to
`t = 5\,s`)

`x_(o) = 0\,ft` and
`x_(f) = -8\,ft`

`\bar v_(i) = (-8\,ft-0\,ft)/(5\,s-1\,s)`

`\bar v_(i) = -2\,(ft)/(s)`

(ii) Ascent (
`t = 5\,s` to
`t = 9\,s`)

`x_(o) = -8\,ft` and
`x_(f) = 0\,ft`

`\bar v_(ii) = (0\,ft-(-8\,ft))/(9\,s-5\,s)`

`\bar v_(ii) = 2\,(ft)/(s)`

(iii) Descent + Ascent (
`t = 1\,s` to
`t = 9\,s`)

`x_(o) = 0\,ft` and
`x_(f) = 0\,ft`

`\bar v_(iii) = (0\,ft-0\,ft)/(9\,s-1\,s)`

`\bar v_(iii) = 0\,(ft)/(s)`

C. Which point on the graph shows the starting location of the diver?

The initial location is when
`t = 0\,s`, which corresponds to the intercept of the line on y-axis.