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

Answer:

$1212.42\ \text{mph}$

Explanation:

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

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

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

$5280\ \text{ft}=5280\times 12=63360\ \text{inches}$

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

$63360\ \text{inches}=63360\times 0.0254=1609.344\ \text{m}$

So

$1\ \text{mile}=1609.344\ \text{m}\\\Rightarrow 1\ \text{m}=\dfrac{1}{1609.34}\ \text{miles}$

$1\ \text{hour}=60\times 60\ \text{seconds}\\\Rightarrow 1\ \text{s}=\dfrac{1}{3600}\ \text{hour}$

$542\ \text{m/s}=\dfrac{\dfrac{542}{1609.34}}{\dfrac{1}{3600}}=1212.42\ \text{mph}$

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