Problem Set 1 (due Jan. 31): Probs. 1-2 [answers in degrees: a) 30^o, b) 120^o, c) 135^o], 1-7, 1-10, 1-21 [ a) 3 x 10⁸ m], 1-23 [4 x 10⁴ km], 1-40, 1-49 [10 m, 100 m, 70 m], 1-54 [1-1/2 km, 60 ^o NW]

Problem 1-2.Express the following angles in radians. For each case, draw a sketch of the angle at the center of a circle and state the result as a ratio of arc length to radius. Your calculator is taboo until you've got the answer. Then be sure you know how to make your calculator generate the correct result.
(a) 90 ° (b) 120 ° (c) 180 °
Similarly, express the following angles in degrees.
(a) p/6 (b) 2p/3 (c) 3p/4

Problem 1-7. What is the physical dimension of each of the following quantities? (a) the density of a piece of metal; (b) the angle between two wooden beams; (c) the area of a farmer's field; (d) the volume of a milk carton.

Problem 1-10. For the vectors A and B in Figure 1.38, sketch the vector sum 2A-B. Which of the vectors labeled (a) through (e) best represents your sketch?

Problem 1-21. (a) A telescope is designed to transmit laser pulses to the Moon and to detect the signal reflected from mirrors left there by the Apollo astronauts. If the time between the transmission of a pulse and the reception of the reflection is 2.433 s, what is the measured distance from the telescope to the mirror on the lunar surface? (b) If the timing system measures time intervals with an uncertainty of 1.5 x 10^-10 sec, what is the corresponding uncertainty in the measured distance to the moon?

Problem 1-23. Erasthenes measured the circumference of the Earth by noting that the Sun was at an angle of 7 ° south of the vertical at Alexandria (Figure 1.41) at the same time that, at Syrene, 800 km south of Alexandria, the sun was observed to be exactly overhead. (Assume that Syrene is directly south of Alexandria.) Based on these data, what is the circumference of the Earth in kilometers?

Problem 1-40. Estimate the order of magnitude of the following quantities. State each step in your reasoning and what data you think it necessary to look up in tables. (a) the volume of gasoline burned annually by private automobiles in the United States; (b) the height of a fence you could build around Tennessee using the stone from the Great Pyramids; (c) the mass of hair swept annually from the floors of U.S. Barbershops; (d) the mass of the Earth; (e) the total length of the interstate highway system; and (f) the number of professional disk jockeys in the United States.

Problem 1-49. Peter and Mary start in the center of a large lawn and run 41 m and 55 m, respectively, each in a straight line, but not necessarily in the same direction. (a) What are the maximum and minimum possible distances between Peter and Mary? Explain your reasoning, using a sketch of their displacements. (b) What is the distance between them if they run in directions at right angles to each other?

Problem 1-54. A delivery truck drives 1.0 km north, 0.50 km east, 1.0 km south, 2.0 km west, 0.50 km northwest, and 0.75 km northeast. Draw a vector diagram showing the truck's journey, and find graphically the magnitude and direction of the truck's displacement vector at the end of the trip.

• Writing out the statement of the problem yourself is NOT required, though I recommend it.
• There MUST be a diagram or drawing with every problem, no matter what the topic. Full credit will NOT be given for a problem unless there is a diagram. The reason for this is that the process of drawing helps you to grasp the essentials of the problem in a way that might be missed if you start calculations immediately.
• Please put a box around the answer, to guide the grader.
• Significant figures as a measure of the accuracy of the result are not a big deal for me. Please give all answers to three significant figures, even if you don't really think the result is that accurate.
• Note that in algebraic calculations, symbols are used rather than putting in numerical values. Wait until the last possible point to substitute in numerical values.