Chapter 8.2, Problem 39E

a.

To determine

To write: the equations that represents the height h (in feet) as a function of time t (in seconds) for both the acorns.

Answer to Problem 39E

Acorn 1:

Acorn 2:

Explanation of Solution

Given information:

The first acorn falls 45 feet.

The second acorn falls 32 feet.

Concept used:

The height (in feet) of a falling object t seconds after it is dropped from an initial height of (in feet) is given by the function:

     ..... (1)

Calculation:

The height h (in feet) for the first acorn as a function of time t (in seconds) is found by substituting in equation (1),

  

The height h (in feet) for the second acorn as a function of time t (in seconds) is found by substituting in equation (1),

  

b.

To determine

To describe: how graphs of the two equations are related.

Answer to Problem 39E

The graph which represents the height of the first acorn is a vertical translation 13 units up of the graph representing the height of the second acorn.

Explanation of Solution

Given information:

The equations that represents the height h (in feet) as a function of time t (in seconds) for both the acorns are:

Acorn 1:

Acorn 2:

Concept used:

Vertical translation:

The graph of is a vertical translation of the graph of f .

The vertical shift is k units up if and k units down if .

Consider the equation representing the height of first acorn:

  

It can be observed that

So, the graph of is a vertical translation of the graph of .

Now, as the shift is 13 units up and so the graph which represents the height of the first acorn is a vertical translation 13 units up of the graph representing the height of the second acorn.