Question

Some gas molecules move at speeds of 542 meters per second. How fast is this in miles per hour? 542 =? 1h Solve by dimensional analysis. Treat as exact numbers: 1 mi = 5280 ft 1 in = 2.54 cm

Answer 1

`1212.42\ \text{mph}`

Step-by-step explanation:

We need to convert
`542\ \text{m/s}` to
`\text{miles/hour}`

`1\ \text{mile}=5280\ \text{ft}`

`1\ \text{ft}=12\ \text{inches}`

`5280\ \text{ft}=5280* 12=63360\ \text{inches}`

`1\ \text{inch}=2.54\ \text{cm}=0.0254\ \text{m}`

`63360\ \text{inches}=63360* 0.0254=1609.344\ \text{m}`

So

`1\ \text{mile}=1609.344\ \text{m}\\\Rightarrow 1\ \text{m}=(1)/(1609.34)\ \text{miles}`

`1\ \text{hour}=60* 60\ \text{seconds}\\\Rightarrow 1\ \text{s}=(1)/(3600)\ \text{hour}`

`542\ \text{m/s}=((542)/(1609.34))/((1)/(3600))=1212.42\ \text{mph}`

The speed of the gas molecules is
`1212.42\ \text{mph}`.