Question

IV. Dimensional Analysis

1) The total length of a football field is 120 yards.
How long is a football field in km? (1 yard = 3 feet, 1
foot = 12 in., 1 in. = 2.54 cm)

Answer 1

0.109728 kilometers

Step-by-step explanation:

To do dimensional analysis, we have to do the unit conversion. We are given all of the conversions, so the first step is to set up the problem:

`120 yards*(3feet)/(1yard)*(12inches)/(1foot)*(2.54cm)/(1inch)*(1m)/(100cm)*(1km)/(1000m)`

To set up a dimensional analysis problem, we need to figure out what unit we need. Since we need kilometers, we need to make sure it ends up in the numerator at the end of the problem. As you can see, each of the other units gets canceled in the setup (for example, there are yards in the numerator and then the denominator of another fraction, so the two cancel each other out). Now, we have the numbers that we need, so we can solve the problem:

`(120*3*12*2.54)/(100*1000)=(10972.8)/(100000)=0.109728 km`

Therefore, our answer is 0.109728 kilometers