Chapter 12.6, Problem 5CYU

a.

To determine

To find: How long does it take for the swing to go forward and back one time.

Answer to Problem 5CYU

It takes $4$ seconds for the swing to go forward and back one time

Explanation of Solution

Given information:

The swing goes forward and reaches its high point of $6$ feet.

And it goes back and reaches $6$ feet backward.

Its lowest point is $2$ feet.

The time it takes to swing from its high point to its low point is $1$ second.

Given

The time it takes to swing from its high point to its low point is $1$ second.

The time taken to swing forwad (i.e from initial position to maximum height) and swing back(i.e maximum height to initial position) is 2 times of time period.

Therefore,

It takes $4$ seconds for the swing to go forward and back one time.

b.

To determine

To find: Graph the height of the swing $h$ as a function of time $t$ .

Explanation of Solution

Given information:

The swing goes forward and reaches its high point of $6$ feet.

And it goes back and reaches $6$ feet backward.

Its lowest point is $2$ feet.

The time it takes to swing from its high point to its low point is $1$ second.

The maximum point is $6$ ft and the minimum point is $2$ ft.

It takes $1$ second to reach from the maximum to the minimum.

So, period is $2$ seconds.

Graph of above situation is