Problem 4: Vectors A, B, and C are shown in Figure 4. The magnitudes of the three vectors are shown in parenthesis. a. What is the resultant vector R = A + B + C? Answer: R = -3.0î + 3.0ĵ b. What is R, the magnitude of R? Answer: R = 4.2 c. What is 8, the angle R makes with respect to the +x-axis? 0 = 180° - 45.0° = 135.0⁰ B (B= 16.2) Figure 4: Vectors for Problem 4. 68.2° y A (A= 10.0) 36.9° 24.0 C(C=9.8) X

Problem 4: Vectors A, B, and C are shown in Figure 4. The magnitudes of the three vectors are shown in parenthesis. a. What is the resultant vector R = A + B + C? Answer: R = -3.0î + 3.0ĵ b. What is R, the magnitude of R? Answer: R = 4.2 c. What is 8, the angle R makes with respect to the +x-axis? 0 = 180° - 45.0° = 135.0⁰ B (B= 16.2) Figure 4: Vectors for Problem 4. 68.2° y A (A= 10.0) 36.9° 24.0 C(C=9.8) X

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 44P: Three displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units,...

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Three displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units, |B|=40.0units, and |C|=30.0units. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Figure P1.44
A vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y component is negative. (c) The x component is negative, and the y component is positive. (d) Both components are negative. (e) More than one answer is possible.
A skater glides along a circular path of radius 5.00 m in clockwise direction. ‘When he coasts around one- half of the circle, starting from the west point, find (a) the magnitude of his displacement vector and (b) how far he actually skated. (c) What is the magnitude of his displacement vector when he skates all the way around the circle and comes back to the west point?
Figure P1.6 shows a frustum of a cone. Match each of the three expressions (a) (r1 + r2)[h2 + (r2 r1)2]1/2, (b) 2(r1 + r2), and (c) h(r12 + r1r2 + r22)/3 with the quantity it describes: (d) the total circumference of the flat circular faces, (e) the volume, or (f) the area of the curved surface. Figure P1.6
A Three vectors all have the same magnitude. The symbol for the magnitude of each of these vectors is M. The first vector A points in the positive x direction. The second vector B points in the negative y direction. The third vector C points in the positive z direction. These three vectors added together are equal to a fourth vector D. What is the magnitude of the fourth vector?
What is the y component of the vector shown in Figure OQ1.9? (a) 3 cm (b) 6 cm (c) 4 cm (d) 6 cm (e) none of those answers Figure OQ1.9 Objective Questions 9 and 10.
The displacement vectors 42.0 cm at 15.0 and 23.0 cm at 65.0 both start from the origin and form two sides of a parallelogram. Both angles are measured counterclockwise from the x axis. (a) Find the area of the parallelogram. (b) Find the length of its longer diagonal.
For the triangle shown in Figure P1.45, what are (a) the length of the unknown side, (b) the tangent of , and (c) the sine of ? Figure P1.45
What is the y component of the vector shown in Figure OQ3.9? (a) 3 cm (b) 6 cm (c) 4 cm (d) 6 cm (e) none of those answers
Let us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are r, u, and t, respectively. Consider the quantity (3u2t). (i) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? (ii) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?
Math Review Given the equations 507 = 147 Vf cos and 377 = 147 Vf sin , find (a) Vf by using the identity cos2 + sin2 = 1, and (b) by using the inverse tangent function. (Note: Some may consider it easier finding the angle first, and then Vf by back substitution.) (See Section 6.4.)
What is the x component of the vector shown in Figure OQ1.9? (a) 3 cm (b) 6 cm (c) 4cm (d) 6cm (e) none of those answers Figure OQ1.9 Objective Questions 9 and 10.