Chapter 5.3, Problem 4RQ

Interpretation Introduction

Interpretation: The time taken to run a 100.m dash needs to be determined if 100.yd dash is completed in 9.8 seconds.

Concept Introduction: The relation between speed, distance and time is as follows:

  $s=\frac{d}{t}$

Here, s is speed, d is distance and t is time.

A conversion factor is defined as number which is used to change one unit to other by either multiplying or dividing. For example, in 1 minute there are 60 seconds and 1 second corresponds to 0.0167 minutes. Thus, for conversion between minutes and seconds, conversion factors used will be $\frac{60\text{ seconds}}{1\text{ minute}}$ or $\frac{0.0167\text{ minutes}}{1\text{ second}}$

Answer to Problem 4RQ

10.72 seconds.

Explanation of Solution

The given distance is 100. yd and time taken to cover this distance is 9.8 seconds. Thus, speed can be calculated as follows:

  $s=\frac{d}{t}$

Putting the values,

  $\begin{array}{c}s=\frac{100\text{ yd}}{9.8\text{ s}}\\ =10.2\text{ yd/s}\end{array}$

Now, the given distance is 100 m and it is mentioned that speed is same thus, time can be calculated as follows:

  $t=\frac{d}{s}$

Putting the values,

  $t=\frac{100\text{ m}}{10.2\text{ yd/s}}$

Here, speed is in yd/s so distance should be converted from m to yd as follows:

Since,

  $1\text{ m}=1.09361\text{ yd}$

Thus, the conversion factor used will be:

  $\frac{1.09361\text{ yd}}{1\text{ m}}$

Putting the value,

  $\begin{array}{c}t=\frac{100\text{ m}\left(\frac{1.09361\text{ yd}}{1\text{ m}}\right)}{10.2\text{ yd/s}}\\ =\frac{109.361\text{ yd}}{10.2\text{ yd/s}}\\ =10.72\text{ s}\end{array}$

Conclusion

Thus, time required to run 100 m dash is 10.72 seconds.