Problems & Exercises

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?

Show that $1\text{.}\text{0 m/s}=3\text{.}\text{6 km/h}$. Hint: Show the explicit steps involved in converting $1\text{.}\text{0 m/s}=3\text{.}\text{6 km/h.}$

Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)

Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)

Tectonic plates are large segments of the Earth's crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

(a) A car speedometer has a $5.0\text{\%}$ uncertainty. What is the range of possible speeds when it reads $\text{90}\text{km/h}$? (b) Convert this range to miles per hour. $\left(\text{1 km}=\text{0.6214 mi}\right)$

(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

State how many significant figures are proper in the results of the following calculations: (a) $\left(\text{106}\text{.}7\right)\left(\text{98}\text{.}2\right)/\left(\text{46}\text{.}\text{210}\right)\left(1\text{.}\text{01}\right)$ (b) ${\left(\text{18}\text{.}7\right)}^2$ (c) $\left(1\text{.}\text{60}\times {\text{10}}^{-\text{19}}\right)\left(\text{3712}\right)$.

(a) If your speedometer has an uncertainty of $2\text{.}0\text{km/h}$ at a speed of $\text{90}\text{km/h}$, what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads $\text{60}\text{km/h}$, what is the range of speeds you could be going?

A person measures his or her heart rate by counting the number of beats in $\text{30}\text{s}$. If $\text{40}\pm 1$ beats are counted in $\text{30}\text{.}0\pm 0\text{.}5\text{s}$, what is the heart rate and its uncertainty in beats per minute?

If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22 mi marathon?

The sides of a small rectangular box are measured to be $1\text{.}\text{80}\pm 0\text{.}\text{01}\text{cm}$, $$$2\text{.}\text{05}\pm 0\text{.}\text{02}\text{cm, and 3}\text{.}1\pm 0\text{.}\text{1 cm}$ long. Calculate its volume and uncertainty in cubic centimeters.

The length and width of a rectangular room are measured to be $3\text{.}\text{955}\pm 0\text{.}\text{005}\text{m}$ and $3\text{.}\text{050}\pm 0\text{.}\text{005}\text{m}$. Calculate the area of the room and its uncertainty in square meters.

How many heartbeats are there in a lifetime?

How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of ${\text{10}}^{-\text{22}}\text{ s}$.)

Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?

(a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?