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Answers are
a) Bx = -2 & By = 2
b) 2.83, 135 degree counter clockwise
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- The same vectors that are shown in Figure P3.6 are shown in Figure P3.42. The magnitudes are F1 = 1.90f, F2 = f, and F3 = 1.4f, where f is a constant. a. Use the coordinate system shown in Figure P3.42 to find R=F1+F2+F3 in component form in terms of f. b. If Rx = 0.33, what is Ry? c. Check your result by comparing your answer to that of Problem 6. FIGURE P3.42A rectangular parallelepiped has dimensions a, b, and c as shown in Figure P3.45. (a) Obtain a vector expression for the face diagonal vector R,. (b) What is the magnitude of this vector? (c) Notice that R, ck, and R, make a right triangle. Obtain a vector expression for the body diagonal vector R2. b Ro R1 Figure P3.45|| For the three vectors shown in Figure P3.53, the vector sum D = Ả + B + Č has components Dx = 2 and D, =0. a. What are the x- and y-components of vector B? b. Write B as a magnitude and a 2 direction. FIGURE P3.53
- IT.0.0a Given an acceleration vector, initial velocity (uo.Vo), and initial position {xo.yo}, find the velocity and position vectors for t2 0. a(t) = (cos t,5 sin t. (Uo Vo) = (0,5) , (Xo.Yo) = (2.0) What is the velc | vector? v(t) =22. Three displacement vectors of a cro- quet ball are shown in Figure P3.22, where A 40.0 units, and |C (a) the resultant in unit-vector nota- 20.0 units, B 30.0 units. Find A. 45.0° tion and (b) the magnitude and direc- tion of the resultant displacement. 45.0 23. (a) Taking A = (6.00 i - 8.00 j) units, QIC B (-8.00 i + 3.00 j) units, and C = (26.0 i + 19.0 j) units, determine a Figure P3.2 and b such that a A + bB + C = 0. (b) A student has learned that a single equation cannot be solved to determine values for more than one unknown in it. How would you explain to him that both a and b can be determined from the single equation used in part (a):| Let à = (3.0 m, 20° south of east), B = (2.0 m, north), and Č= (5.0 m, 70° south of west). a. Draw and label Á, B, and Č with their tails at the origin. Use a coordinate system with the x-axis to the east. b. Write the x- and y-components of vectors Á, B, and Č. c. Find the magnitude and the direction of D = Ả + B + Č.
- I| Suppose E = 2Á + 3B _where vector A has components A = 5, A, = 2 and vector B has components By=-3, B,= -5. a. What are the x- and y-components of vector É? b. Draw a coordinate system and on it show vectors Ã, B, and Ē. c. What are the magnitude and direction of vector É?5.3. a. Two position vectors are seen. Draw the displacement 2- on a separate sheet. HELP: Use the tip-to-tip drawing rule 7₂ b. Suppose has magnitude 6 and 2 has magnitude 2. What is the magnitude of Ar=2-71 c. Two velocity vectors are seen. Draw the difference 2-₁. Suppose ₁ has magnitude 5 and 2 has magnitude 10. What is the magnitude of A? 32 V1 I| Suppose D =Á – B where vector Á has components A, = 5, A, = 2 and vector B has components Bz= -3, B,=-5. a. What are the x- and y-components of vector D? b. Draw a coordinate system and on it show vectors Á, B, and Ď. c. What are the magnitude and direction of vector Ď?
- | Suppose Č= Á + B where vector A has components A, = 5, A, = 2 and vector B has components B,= -3, B,= -5. a. What are the x- and y-components of vector C? b. Draw a coordinate system and on it show vectors Á, B, and Č. c. What are the magnitude and direction of vector Č? yVector A has a magnitude of 8 units and makes an angle of 45.0 degrees with the positive x-axis. Vector B also has a magnitude of 8 units and is directed along the negative x-axis. The magnitude of A-B is: 1. on 4v2 45 4V7 Select one: O A. 14.78 O B. 4.65 O C. 8.22 O D. None O E. 12.44Which combination of the vectors shown has the largest magnitude? В. В+А-С D. В- A-C A. Ã + B +C С. А - В+с 1- FIGURE Q3.20