Feet per second to Millimeters per hour conversion

How to convert feet per second to millimeters per hour?

To convert a speed from feet per second (ft/s) to millimeters per hour (mm/h), you need to know the following conversions: 1 foot (ft) = 304.8 millimeters (mm) 1 hour = 3600 seconds

Given 1 ft/s, we perform the conversion as follows:

1. Convert feet to millimeters: $\text{1 ft/s} \times 304.8 \text{ mm/ft} = 304.8 \text{ mm/s}$

2. Convert seconds to hours: $\text{304.8 mm/s} \times 3600 \text{ s/h} = 1,097,280 \text{ mm/h}$

So, 1 ft/s is equivalent to 1,097,280 mm/h.

Real-World Examples

Example 1: Human Walking Speed

Average walking speed is about 3.1 miles per hour (mph): 1 mile = 5280 feet, so:

$3.1 \text{ mph} = 3.1 \times 5280 \text{ ft/h} = 16,368 \text{ ft/h}$

Convert to ft/s: $16,368 \text{ ft/h} ÷ 3600 \text{ s/h} = 4.5467 \text{ ft/s}$

Then convert to mm/h using the above method: $4.5467 \text{ ft/s} \times 304.8 \text{ mm/ft} \times 3600 \text{ s/h} = 4,992,400.176 \text{ mm/h}$

Example 2: Speed of Light

The speed of light is approximately 299,792,458 meters per second: 1 meter = 3.28084 feet, so:

$299,792,458 \text{ m/s} \times 3.28084 \text{ ft/m} = 983,571,056 \text{ ft/s}$

Convert to mm/h: $983,571,056 \text{ ft/s} \times 304.8 \text{ mm/ft} \times 3600 \text{ s/h} = 1.07722 \times 10^{16} \text{ mm/h}$

Example 3: Sprinting Speed of Usain Bolt

Usain Bolt's maximum recorded speed during a sprint is about 27.8 mph: $27.8 \times 5280 \text{ ft/h} = 146,784 \text{ ft/h}$

Convert to ft/s: $146,784 \text{ ft/h} ÷ 3600 \text{ s/h} = 40.7733 \text{ ft/s}$

Then convert to mm/h: $40.7733 \text{ ft/s} \times 304.8 \text{ mm/ft} \times 3600 \text{ s/h} = 44,063,318.24 \text{ mm/h}$

These conversions demonstrate how speeds in feet per second translate to millimeters per hour, showing the scale of the units in different contexts from everyday walking to the speed of light.