Chapter 3, Problem 98A

Interpretation Introduction

Interpretation : The speed in meters per second is to be calculated.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 98A

The speed in meters per second is $3.1\times {10}^1\text{m/s}$ .

Explanation of Solution

Given information :

The speed of a cheetah is $112\text{km/hr}$ .

It is known that $1\text{km}={10}^3\text{m}$ , $1\text{hr}=60\text{mins}$ and $1\text{min}=60\text{s}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is $\text{km/hr}\to \text{m/s}$ .

The conversion of the value is given as:

  $\begin{array}{c}112\text{km/hr}\text{=}\frac{112\cancel{\text{km}}}{\cancel{\text{hr}}}\times \frac{{10}^3\text{m}}{1\cancel{\text{km}}}\times \frac{1\cancel{\text{hr}}}{60\cancel{\text{min}}}\times \frac{1\cancel{\text{min}}}{60\text{s}}\left(\because 1\text{km}={10}^3\text{m},1\text{hr}=60\text{mins},1\text{min}=60\text{s}\right)\\ =0.0311\times {10}^3\text{m/s}\\ \text{=}\text{3}\text{.1}\times {10}^1\text{m/s}\end{array}$

Conclusion

The speed in meters per second is $3.1\times {10}^1\text{m/s}$ .