ssm_ch03 - Chapter 3 Student Solutions Manual 1. A vector a...

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Chapter 3 – Student Solutions Manual 1. A vector can be represented in the magnitude-angle notation ( a , θ ), where a G 22 x y aa a = + is the magnitude and 1 tan y x a a ⎛⎞ = ⎜⎟ ⎝⎠ is the angle makes with the positive x axis. a G (a) Given A x = 25.0 m and A y = 40.0 m, ( 25.0 m) (40.0 m) 47.2 m A =− + = (b) Recalling that tan = tan ( + 180°), tan –1 [40/ (– 25)] = – 58° or 122°. Noting that the vector is in the third quadrant (by the signs of its x and y components) we see that 122° is the correct answer. The graphical calculator “shortcuts” mentioned above are designed to correctly choose the right possibility. 3. The x and the y components of a vector G a lying on the xy plane are given by cos , sin xy = = where is the magnitude and is the angle between || = G G a and the positive x axis. (a) The x component of is given by a G a x = 7.3 cos 250° = – 2.5 m. (b) and the y component is given by a y = 7.3 sin 250° = – 6.9 m. In considering the variety of ways to compute these, we note that the vector is 70° below the – x axis, so the components could also have been found from a x = – 7.3 cos 70° and a y = – 7.3 sin 70°. In a similar vein, we note that the vector is 20° to the left from the – y axis, so one could use a x = – 7.3 sin 20° and a y = – 7.3 cos 20° to achieve the same results.
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ssm_ch03 - Chapter 3 Student Solutions Manual 1. A vector a...

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