Question

Convert 60 mph (mi/h) to ft/s. Select the correct dimensional analysis set up only.

Option 1: (60 mi/h) x (1 h/3600 s) x (5280 ft/1 mi)

Option 2: (60 mi/h) x (1 h/3600 s) x (1 mi/5280 ft)

Option 3: (60 mi/h) x (1 s/3600 h) x (1 mi/5280 ft)

Option 4: (60 mi/h) x (3600 s/1 h) x (1 mi/5280 ft)

Answer 1

The correct dimensional analysis setup to convert 60 mph to ft/s is Option 1: (60 mi/h) x (1 h/3600 s) x (5280 ft/1 mi). This setup correctly cancels out the hours and miles, leaving the speed in the desired units of feet per second.

Step-by-step explanation:

To convert 60 mph (miles per hour) to ft/s (feet per second), we need to use dimensional analysis to ensure the correct relationship between units. The proper conversion factors will cancel out the original units and leave us with the desired units.

The correct set up for dimensional analysis to convert 60 mph to ft/s is as follows:

Option 1: (60 mi/h) x (1 h/3600 s) x (5280 ft/1 mi)

This option uses the conversion factor of 1 hour equals 3600 seconds to convert the time units from hours to seconds. It also uses the conversion factor of 5280 feet equals 1 mile to convert the distance units from miles to feet.

The first part of the conversion cancels out the hours, and the second part cancels out the miles, leaving the speed in feet per second. Therefore, the correct dimensional analysis set up is Option 1.