Michael+Hays

CQ8: Which of the following quantities (if any) can be considered a vector: (a) the number of people attending a football game, (b) the number of days in a month, and (c) the number of pages in a book? Explain your reasoning.

The answer is none of the above. A vector is something that is described in 2 different quantities, for example distance and direction. Each of (a), (b), and (c) is described in a single quantity, which is a scalar.

P3: Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in (a) kilometers per hour (ki/h) and (b) meters per second (m/s)?

The speed is 54.7 (ki/h) and 15.2 (m/s). This can be reached by dimentional analysis, where you convert miles to kilometers and meters, then hours to seconds.

P31: Vector **A** points along the +y axis and has a magnitude of 100.0 units. Vector **B** points at an angle of 60.0° above the +x axis and has a magnitude of 200.0 units. Vector **C** points along the +x axis and has a magnitude of 150.0 units. Which vector has (a) the largest x component and (b) the largest y component?

Vector **C** has the largest x component (at 150.0 units) and Vector **B** has the largest y component (at 100sqrt(3) units).

P42: Multiple-Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 16.0 m, B = 11.0 m, C = 12.0 m, and D = 26.0 m. Determine the magnitude and directional angle for the resultant that occurs when these vectors are added together.

The magnitude for the resulting angle is 13.1577 and the direction is 51.7133° south of west.