Physical Units and Conversions

Problems

1) A woman once survived a fall of over six miles without a parachute when her plane exploded. Suppose a hapless individual is falling from a height of 5 miles and 1320 yards. What is this distance in meters?

2) A bicyclist in the Tour de France has a speed of 31.6 miles per hour (mi/h) on a flat section of the road. What is this speed in (a) kilometers per hour (km/h), and (b) meters per second (m/s)?

3) Azelastine hydrochloride is an antihistamine nasal spray. A standard size container holds one fluid ounce (oz.) of the liquid. You are searching for this medication in a European drugstore and are asked how many milliliters (mL) there are in one fluid ounce. Using the following conversion factors, determine the number of milliliters in a volume of 1.25 fluid ounces: 1 gallon (gal) = 128 oz., 3.785 x 10-3 cubic meters (m3) = 1 gal, 1 liter = 10-3 m3.

4) The following are dimensions of various physical parameters. Here [L], [T], and [M] denote, respectively, dimensions of length, time, and mass.

Distance (x) [L]

Time (t) [T]

Mass (m) [M]

Speed (v) [L]/[T]

Acceleration (a) [L]/[T]2

Force (F) [M][L]/[T]2

Energy (E) [M][L]2/[T]2

Which of the following equations are dimensionally correct?

(Indicate one or more choices.)

F = ma

x = (1/2)at2

E = (1/2)mv2

E = max2

v = sqrt(2Fx/m)

5) The depth of the ocean is sometimes measured in fathoms (1 fathom = 6 feet). Distance on the surface of the ocean is sometimes measured in nautical miles (1 nautical mile = 6076 feet). The water beneath a surface rectangle 1.7 nautical miles by 2.1 nautical miles has a depth of 19 fathoms. Find the volume of water (in cubic meters) beneath this rectangle.

6) You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 2.37 ° above the horizontal. Approximately how far (in kilometers) are you from the base of the arch?

7) The gondola ski lift at a ski resort has a cable which is 2600 m long. On average, the ski lift rises 21° above the horizontal. How high is the top of the ski lift relative to the base? Assume the cable does not sag.

8) A highway is to be built between two towns, one of which lies 36.0 km east and 42.0 km north of the other. (a) What is the shortest length of highway that can be built between the two towns, and (b) at what angle would this highway be directed, as a positive angle with respect to due east?

9) The drawing shows sodium and chlorine ions positioned at the corners of a cube that is part of the crystal structure of sodium chloride (common table salt). The edge of the cube is 0.281 nm (1 nm = 1 nanometer = 10–9 m) in length. (a) Find the distance (in nanometers) between the sodium ion located at one corner of the cube and the chloride ion located on the diagonal at the opposite corner. (b)What is the value of the angle in the drawing shown?