1.3 Unit conversion  (Page 3/4)

The volume of Earth is on the order of 10 ²¹ m ³ . (a) What is this in cubic kilometers (km ³ )? (b) What is it in cubic miles (mi ³ )? (c) What is it in cubic centimeters (cm ³ )?

The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?

A car is traveling at a speed of 33 m/s. (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h speed limit?

In SI units, speeds are measured in meters per second (m/s). But, depending on where you live, you’re probably more comfortable of thinking of speeds in terms of either kilometers per hour (km/h) or miles per hour (mi/h). In this problem, you will see that 1 m/s is roughly 4 km/h or 2 mi/h, which is handy to use when developing your physical intuition. More precisely, show that (a) $1.0\text{m/s}=3.6\text{km/h}$ and (b) $1.0\text{m/s}=2.2\text{mi/h}.$

American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 m = 3.281 ft.)

Soccer fields vary in size. A large soccer field is 115 m long and 85.0 m wide. What is its area in square feet? (Assume that 1 m = 3.281 ft.)

What is the height in meters of a person who is 6 ft 1.0 in. tall?

Mount Everest, at 29,028 ft, is the tallest mountain on Earth. What is its height in kilometers? (Assume that 1 m = 3.281 ft.)

The speed of sound is measured to be 342 m/s on a certain day. What is this measurement in kilometers per hour?

Tectonic plates are large segments of Earth’s crust that move slowly. Suppose one such plate has an average speed of 4.0 cm/yr. (a) What distance does it move in 1.0 s at this speed? (b) What is its speed in kilometers per million years?

The average distance between Earth and the Sun is $1.5\times {10}^{11}\text{m.}$ (a) Calculate the average speed of Earth in its orbit (assumed to be circular) in meters per second. (b) What is this speed in miles per hour?

The density of nuclear matter is about 10 ¹⁸ kg/m ³ . Given that 1 mL is equal in volume to cm ³ , what is the density of nuclear matter in megagrams per microliter (that is, $\text{Mg/}\mu \text{L}$ )?

The density of aluminum is 2.7 g/cm ³ . What is the density in kilograms per cubic meter?

A commonly used unit of mass in the English system is the pound-mass, abbreviated lbm, where 1 lbm = 0.454 kg. What is the density of water in pound-mass per cubic foot?

A furlong is 220 yd. A fortnight is 2 weeks. Convert a speed of one furlong per fortnight to millimeters per second.

It takes $2\pi$ radians (rad) to get around a circle, which is the same as 360°. How many radians are in 1°?

Light travels a distance of about $3\times {10}^8\text{m/s.}$ A light-minute is the distance light travels in 1 min. If the Sun is $1.5\times {10}^{11}\text{m}$ from Earth, how far away is it in light-minutes?

A light-nanosecond is the distance light travels in 1 ns. Convert 1 ft to light-nanoseconds.

An electron has a mass of $9.11\times {10}^{\mathrm{-31}}\text{kg.}$ A proton has a mass of $1.67\times {10}^{\mathrm{-27}}\text{kg}\text{.}$ What is the mass of a proton in electron-masses?

A fluid ounce is about 30 mL. What is the volume of a 12 fl-oz can of soda pop in cubic meters?