Q6PE - College Physics (Urone)

Question

What is the height in meters of a person who is \({\bf{6}}{\rm{ }}{\bf{ft}}{\rm{ }}{\bf{1}}.{\bf{0}}{\rm{ }}{\bf{in}}\) tall? (Assume that \({\bf{1}}{\rm{ }}{\bf{meter}}\) equals \({\bf{39}}.{\bf{37}}{\rm{ }}{\bf{in}}\).)

Step-by-Step Solution

Answer

The height of the person in meters is \({\bf{1}}.{\bf{85}}{\rm{ }}{\bf{m}}\).

Step 1: Stating given and known data

Person’s height, \(h = {\bf{6}}{\rm{ }}{\bf{ft}}{\rm{ }}{\bf{1}}.{\bf{0}}{\rm{ }}{\bf{in}}\).

1 m = 39.37 inches

The relation between a foot and an inch is

\(1{\rm{ foot}} = 12{\rm{ inch}}\)es

Step 2: Calculating height of person in inches:

Convert the height of the person to inches.

\(\begin{array}{c}6{\rm{ ft }}1.0{\rm{ inches }} = \left( {6{\rm{ ft}}} \right)\left( {\frac{{12{\rm{ inches}}}}{{1{\rm{ ft}}}}} \right) + 1{\rm{ inch}}\\ = 72{\rm{ inches}} + 1{\rm{ inch}}\\ = 73{\rm{ inches}}\end{array}\)

Therefore, the height of the person in meters is \(73{\rm{ inches}}\).

Step 3: Calculating height of person in meters

The relation between meter and inches is

\(1{\rm{ m}} = 39.37{\rm{ inches}}\) 

The height of the person in meter is

\(\begin{array}{c}{\bf{73}}{\rm{ }}{\bf{inches}} = \left( {{\bf{73}}{\rm{ }}{\bf{inches}}} \right)\left( {\frac{{{\bf{1}}{\rm{ }}{\bf{m}}}}{{{\bf{39}}.{\bf{37}}{\rm{ }}{\bf{inches}}}}} \right)\\ = {\bf{1}}.{\bf{85}}{\rm{ }}{\bf{m}}\end{array}\)

Hence, the height of person in meters is \({\bf{1}}.{\bf{85}}{\rm{ }}{\bf{m}}\).