Question

If an airplane can travel at 20,000 miles per hour, how many meters per second does it travel? Knowing that: 1 mi 1.609 km​

Answer 1

Answer: 8,938
`(8)/(9)` or 8,938.8889 meters per second

Explanation:

To solve this problem, we will use a process called dimensional analysis (that you have probably done many times without realizing it).

What is dimensional analysis? Let's say you know there are 12 inches in a foot, and you want to know how many inches are in 2 feet. 12 * 2 = 24 inches in a foot, that's dimensional analysis!

Here is the process you would take to solve your problem:

➜ If we have the units
`(hour)/(hour)`, they "cancel" out to become one. This way, we make sure we end up with the correct units,
`(meters)/(second)`.

➜ We take units we know, such as 3,600 seconds in an hour, and multiply them by the original value until we end up with the measurement we want.

`\displaystyle 20,000\; (miles)/(hour)*(1 \;hour)/(3,600\; seconds) *(1,609\;meters)/(1\;mile)=(20,000*1*1,609\;meters)/(3,600\;seconds) =(32,180,000\;meters)/(3,600\;seconds) = 8,938.89\; (meters)/(second)`

In other words;

8,938.89 meters per second