Q50P - Fundamentals Of Physics

Question

You receive orders to sail due east for $24.5\mathbf{ }\mathbf{mi}$  to put your salvage ship directly over a sunken pirate ship. However, when your divers probe the ocean floor at that location and find no evidence of a ship, you radio back to your source of information, only to discover that the sailing distance was supposed to be $24.5\mathbf{ }\mathbf{nautical}\mathbf{ }\mathbf{miles}$ , not regular miles. Use the Length table in Appendix D to calculate how far horizontally you are from the pirate ship in kilometers.

Step-by-Step Solution

Answer

The difference between the two given locations is $5.95 \mathrm{km}$ .

Step 1: Given data

The sailing distance is $24.5 \mathrm{nautical} \mathrm{miles}$ .

Step 2: Understanding the conversion factor

In unit conversion, conversion factors are used to converts the units of measure for the same quantity. Use the conversion factors to covert the distance from nautical miles to kilometers.

Step 3: Determination of the distances in kilometers

By using length conversion given in Appendix D, convert both miles and nautical miles into kilometers. After that, find the difference between the distances to find the difference between the two locations.

 

So, first of all, find both the distances in kilometers. 

As given in Appendix D,

$$\begin{gathered} 1 \mathrm{mile}=1.609 \mathrm{km} \\ 1 \mathrm{nautical} \mathrm{mile}=1.852 \mathrm{km} \\ \mathrm{find} \mathrm{the} \mathrm{distance} \mathrm{in} \mathrm{miles}. \\ 24.5 \mathrm{miles}=24.5 \mathrm{miles} \times \frac{1.60 \mathrm{km}}{1 \mathrm{mile}} \\ =39.42 \mathrm{km} \end{gathered}$$

Thus, $24.5 \mathrm{miles}$ is equivalent to $39.42 \mathrm{km}$

 

Find the distance in nautical miles.

$$\begin{gathered} 24.5 \mathrm{nautical} \mathrm{mile}=24.5 \mathrm{miles}\times \frac{1.852 \mathrm{km}}{1 \mathrm{mile}} \\ =45.37 \mathrm{km} \end{gathered}$$

 

Thus, $24.5 \mathrm{miles}$ is equivalent to $45.37 \mathrm{km}$.

Step 4: Determination of the difference between two distances

The difference between the distance covered in nautical miles and miles is, 

 

$45.37-39.42=5.95 \mathrm{km}$

 

Thus, the difference between the two distance is $5.95 \mathrm{km}.$