Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Textbook Question
Chapter 3, Problem 35P
Vector
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Three displacement vectors of a croquet ball are shown in the figure, where |A 19.0 units, 181 = 45.0 units, and ICI = 30.0 units.
B
45.0⁰
45.0
C
-x
(a) Find the resultant in unit-vector notation.
R 53.19i+24.04j x units
(b) Find the magnitude and direction of the resultant displacement.
magnitude 60.738
unit(s)
direction
29.173
counterclockwise from the +x axis
Figure E1.37
y
A (3.60 m)
70.0°
X
30.0°
B (2.4 m)
| Vector Á
3.02 – 4.0k. (a) Construct a unit vector that
3
is parallel to A. (b) Construct a unit vector that is antiparallel to A.
(c) Construct two unit vectors that are perpendicular to A and that have
no y-component.
To visit your favorite ice cream shop, you must travel 420 mm west on Main Street and then 970 mm south on Division Street.
a) Find the total distance you traveled.
Express your answer to two significant figures and include appropriate units.
b) Choose the correct displacement vector written in unit vector notation, taking the x^x^ direction to be east and the y^y^ direction to be north.
r⃗ =r→=
Choose the correct displacement vector written in unit vector notation, taking the direction to be east and the direction to be north.
Chapter 3 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 3.2 - Which of the following are vector quantities and...Ch. 3.3 - Prob. 3.2QQCh. 3.3 - If vector B is added to vector A, which two of the...Ch. 3.4 - Choose the correct response to make the sentence...Ch. 3.4 - Prob. 3.5QQCh. 3 - What is the magnitude of the vector...Ch. 3 - A vector lying in the xy plane has components of...Ch. 3 - Figure OQ3.3 shows two vectors D1 and D2. Which of...Ch. 3 - The cutting tool on a lathe is given two...Ch. 3 - The magnitude of vector A 8 km, and the magnitude...
Ch. 3 - Prob. 6OQCh. 3 - Yes or no: Is each of the following quantities a...Ch. 3 - What is the y component of the vector (3i-8k)m/s?...Ch. 3 - What is the x component of the vector shown in...Ch. 3 - What is the y component of the vector shown in...Ch. 3 - Prob. 11OQCh. 3 - A submarine dives from the water surface at an...Ch. 3 - Prob. 13OQCh. 3 - Is it possible to add a vector quantity to a...Ch. 3 - Can the magnitude of a vector have a negative...Ch. 3 - A book is moved once around the perimeter of a...Ch. 3 - Prob. 4CQCh. 3 - Prob. 5CQCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Two points in the xy plane have Cartesian...Ch. 3 - Prob. 4PCh. 3 - The polar coordinates of a certain point are (r =...Ch. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Why is the following situation impossible? A...Ch. 3 - A force F1 of magnitude 6.00 units acts on an...Ch. 3 - The displacement vectors A and B shown in Figure...Ch. 3 - Three displacements are A=200m due south, B=250m...Ch. 3 - A roller-coaster car moves 200 ft horizontally and...Ch. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Prob. 17PCh. 3 - A person walks 25.0 north of east for 3.10 km. How...Ch. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - While exploring a cave, a spelunker starts at the...Ch. 3 - Use the component method to add the vectors A and...Ch. 3 - Prob. 23PCh. 3 - A map suggests that Atlanta is 730 miles in a...Ch. 3 - Your dog is running around the grass in your back...Ch. 3 - Given the vectors A=2.00i+6.00j and B=3.00i2.00j,...Ch. 3 - A novice golfer on the green takes three strokes...Ch. 3 - A snow-covered ski slope makes an angle of 35.0...Ch. 3 - The helicopter view in Fig. P3.15 shows two people...Ch. 3 - In a game of American football, a quarterback...Ch. 3 - Prob. 31PCh. 3 - Vector A has x and y components of 8.70 cm and...Ch. 3 - The vector A has x, y, and z components of 8.00,...Ch. 3 - Prob. 34PCh. 3 - Vector A has a negative x component 3.00 units in...Ch. 3 - Given the displacement vectors A=(3i4j+4k)m and...Ch. 3 - Prob. 37PCh. 3 - Three displacement vectors of a croquet ball are...Ch. 3 - A man pushing a mop across a floor causes it to...Ch. 3 - Figure P3.28 illustrates typical proportions of...Ch. 3 - Express in unit-vector notation the following...Ch. 3 - radar station locates a sinking ship at range 17.3...Ch. 3 - Prob. 43PCh. 3 - Why is the following situation impossible? A...Ch. 3 - Review. You are standing on the ground at the...Ch. 3 - Prob. 46PCh. 3 - In an assembly operation illustrated in Figure...Ch. 3 - A fly lands on one wall of a room. The lower-left...Ch. 3 - As she picks up her riders, a bus driver traverses...Ch. 3 - A jet airliner, moving initially at 300 mi/h to...Ch. 3 - A person going for a walk follows the path shown...Ch. 3 - Find the horizontal and vertical components of the...Ch. 3 - Review. The biggest stuffed animal in the world is...Ch. 3 - An air-traffic controller observes two aircraft on...Ch. 3 - In Figure P3.55, a spider is resting after...Ch. 3 - The rectangle shown in Figure P3.56 has sides...Ch. 3 - Prob. 57APCh. 3 - A ferry transports tourists between three islands....Ch. 3 - Two vectors A and B have precisely equal...Ch. 3 - Two vectors A and B have precisely equal...Ch. 3 - Prob. 61APCh. 3 - Prob. 62APCh. 3 - Prob. 63APCh. 3 - Prob. 64APCh. 3 - A rectangular parallelepiped has dimensions a, b,...Ch. 3 - Vectors A and B have equal magnitudes of 5.00. The...Ch. 3 - A pirate has buried his treasure on an island with...
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- 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.arrow_forwardX is an unknown vector satisfying the following relations involving the known vectors A and B and the scalar ϕ, A × X = B, A · X = ϕ. Express X in terms of A, B, ϕ, and the magnitude of A.arrow_forwardThree 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 P1.44arrow_forward
- A vector A has components Ax = 5.00 m and Ay = 9.00 m. Find (a) the magnitude and (b) the direction of the vector.arrow_forwardFigure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.arrow_forwardWhat is the y component of the vector (3i8k) m/s? (a) 3 m/s (b) 8 m/s (c) 0 (d) 8 m/s (e) none of those answersarrow_forward
- The resultant vector R=2AB2C has zero magnitude. Vector A has an x component of 4.60 m and a y component of 12.1 m. and vector B has an x component of 3.00 m and a y component of 4.00 m. What are the x and y components of vector C? (All of these are two-dimensional vectors.)arrow_forwardThe magnitudes of two vectors A and B are 12 units and 8 units, respectively. What are the largest and smallest possible values for the magnitude of the resultant vector R = A + B? (a) 14.4 and 4 (b) 12 and 8 (c) 20 and 4 (d) none of these.arrow_forwardIf A + B = 0, the corresponding components of the two vectors Aand Bmust be (a) equal, (b) positive, (c) negative, (d) of opposite sign.arrow_forward
- Show that (2arr+2brr)dt=ar2+br2+const. where r is the vector from the origin to the point (x1, x2, x3). The quantities r and r are the magnitudes of the vectors r and r, respectively, and a and b are constants.arrow_forwardFind (a) the x- and (b) y-components of R = 2A B if A has components Ax = 15.0 m and Ay = 12.0 m whereas B has components Bx = 24.0 m and By = 8.00 m. (See Section 3.2.)arrow_forwardFor what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?arrow_forward
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