Chapter 11.4, Problem 51PPS

(a)

To determine

To write the expression for the number of meters the room moves per second for $27$ rotations per minute.

Answer to Problem 51PPS

The expression for the room movement in meters per second for $27$ rotations per minute is $27\times 2\times \frac{22}{7}\times 3.1\times 60$

Explanation of Solution

Given:

Radius $=$ $3.1$ meters

Formula Used:

Circumference of a Circle $=$ $2\pi r$

  $1$ min $=$ $60$ seconds

Calculation:

Given:

Radius $=$ $3.1$ meters

Using the above formula, we have:

Circumference of a Circle $=$ $2\pi r$

Circumference of a Circle $=$ $2\times \frac{22}{7}\times 3.1$

For $27$ rotations, we have:

Circumference of a Circle $=$ $27\times 2\times \frac{22}{7}\times 3.1$ meters

Number of meters in $1$ sec $=$ $27\times 2\times \frac{22}{7}\times 3.1\times 60$ meters per second

Conclusion:

Hence, the expression for the room movement in meters per second for $27$ rotations per minute is $27\times 2\times \frac{22}{7}\times 3.1\times 60$

(b)

To determine

To simplify the expression for the number of meters the room moves per second for $27$ rotations per minute.

Answer to Problem 51PPS

The room movement is $27\times 2\times \frac{22}{7}\times 3.1\times 60$ meters per second.

Explanation of Solution

Given:

Radius $=$ $3.1$ meters

Formula Used:

Circumference of a Circle $=$ $2\pi r$

  $1$ min $=$ $60$ seconds

Calculation:

Given:

Radius $=$ $3.1$ meters

Using the above formula, we have:

Circumference of a Circle $=$ $2\pi r$

Circumference of a Circle $=$ $2\times \frac{22}{7}\times 3.1$

For $27$ rotations, we have:

Circumference of a Circle $=$ $27\times 2\times \frac{22}{7}\times 3.1$ meters

Number of meters in $1$ sec $=$ $27\times 2\times \frac{22}{7}\times 3.1\times 60$ meters per second

Solving further, we have:

Number of meters in $1$ sec $=$ $31,566.85$ meters per second.

Conclusion:

Hence, the room movement is $31,566.85$ in meters per second.