Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 1, Problem 54P
(a)
To determine
Draw a map of the successive displacement.
(b)
To determine
The total distance of the riders travel in a bus.
(c)
To determine
The magnitude and direction of the total displacement.
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Displacement d1 is in the yz plane 5 9.9° from the positive direction of the y axis, has a positive z component, and has a magnitude of 3.39 m. Displacement d2 is in the xz plane 20.8° from the positive direction of the x axis, has a positive z component, and has magnitude 1.02 m. What are (a) d1•d2, and (b) the angle between d1 and d2?
A student takes a much needed break from her studies and wanders around in the Arnold Arboretum.
First, the student travels through a displacement
N (+y)
=
= 400 m, directed 40.0° W of S.
%3D
Then the student undergoes a displacement
D2= 800 m, directed 30.0° N of W.
E (+x)
%3D
Thus, the student undergoes a resultant displacement R=D, +D, ·
In the following, assume that the +y direction is defined as due North and
that the +x direction is defined as due East, as shown in the figure.
16. True or False: Displacement D, has a scalar x component equal to 306 m?
A. True.
B. False.
17. Displacement D, has a y component-vector equal to
A. 400 m.
B. - 400 m.
C. 693 m j.
î .
E. 400 m j.
D. 693 m
18. True or False: D1,x is positive while D2,x is negative?
A. True.
B. False.
19. The student's resultant displacement R has a magnitude of
A. 1044 m.
B. - 856 m.
C. 955 m.
D. 1200 m.
E. 400 m.
20. The student's resultant displacement is directed
A. 5.63° N of W.
B. 84.4° N of W.
C. 5.63° S of W.
D.…
Displacement d1 is in the yz plane 5 9.9° from the positive direction of the y axis, has a positive z component, and has a magnitude of 3.39 m. Displacement d2 is in the xz plane 20.8° from the positive direction of the x axis, has a positive z component, and has
magnitude 1.02 m. What are (a) d1•d2, (b)the x component of d1 x d2 (c)the y component of d1 x d2 (d) the z component of
dı x d2, and (e) the angle between d1 and d2?
Chapter 1 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 1.2 - True or False: Dimensional analysis can give you...Ch. 1.3 - The distance between two cities is 100 mi. What is...Ch. 1.7 - Which of the following are vector quantities and...Ch. 1.8 - Prob. 1.4QQCh. 1.8 - Prob. 1.5QQCh. 1.9 - Choose the correct response to make the sentence...Ch. 1.9 - If at least one component of a vector is a...Ch. 1.9 - If A + B = 0, the corresponding components of the...Ch. 1 - Answer each question yes or no. Must two...Ch. 1 - The price of gasoline at a particular station is...
Ch. 1 - Rank the following five quantities in order from...Ch. 1 - What is the y component of the vector (3i8k) m/s?...Ch. 1 - Prob. 5OQCh. 1 - Prob. 6OQCh. 1 - One student uses a meterstick to measure the...Ch. 1 - Prob. 8OQCh. 1 - What is the x component of the vector shown in...Ch. 1 - What is the y component of the vector shown in...Ch. 1 - Prob. 11OQCh. 1 - Prob. 12OQCh. 1 - Figure OQ1.13 shows two vectors D1 and D2. Which...Ch. 1 - A vector points from the origin into the second...Ch. 1 - Prob. 15OQCh. 1 - Prob. 16OQCh. 1 - Prob. 1CQCh. 1 - Prob. 2CQCh. 1 - Prob. 3CQCh. 1 - Prob. 4CQCh. 1 - A book is moved once around the perimeter of a...Ch. 1 - Prob. 6CQCh. 1 - Prob. 7CQCh. 1 - Prob. 8CQCh. 1 - Prob. 1PCh. 1 - Prob. 2PCh. 1 - Prob. 3PCh. 1 - Prob. 4PCh. 1 - Prob. 5PCh. 1 - Figure P1.6 shows a frustum of a cone. Match each...Ch. 1 - Prob. 7PCh. 1 - Prob. 8PCh. 1 - Prob. 9PCh. 1 - Prob. 10PCh. 1 - Prob. 11PCh. 1 - Prob. 12PCh. 1 - Prob. 13PCh. 1 - Let AI represent the density of aluminum and Fe...Ch. 1 - Assume it takes 7.00 min to fill a 30.0-gal...Ch. 1 - Prob. 16PCh. 1 - Find the order of magnitude of the number of...Ch. 1 - Prob. 18PCh. 1 - To an order of magnitude, how many piano tuners...Ch. 1 - Prob. 20PCh. 1 - Prob. 21PCh. 1 - Carry out the arithmetic operations (a) the sum of...Ch. 1 - Prob. 23PCh. 1 - Prob. 24PCh. 1 - A sidewalk is to be constructed around a swimming...Ch. 1 - Prob. 26PCh. 1 - Prob. 27PCh. 1 - Prob. 28PCh. 1 - Prob. 29PCh. 1 - Two points in the xy plane have Cartesian...Ch. 1 - The polar coordinates of a point are r = 5.50 m...Ch. 1 - Prob. 32PCh. 1 - Prob. 33PCh. 1 - Prob. 35PCh. 1 - A plane flies from base camp to Lake A, 280 km...Ch. 1 - A roller-coaster car moves 200 ft horizontally and...Ch. 1 - Prob. 38PCh. 1 - Prob. 39PCh. 1 - Find the horizontal and vertical components of the...Ch. 1 - Prob. 41PCh. 1 - Vector B has x, y, and z components of 4.00, 6.00,...Ch. 1 - Prob. 43PCh. 1 - Three displacement vectors of a croquet ball are...Ch. 1 - Prob. 45PCh. 1 - Vector A has x and y components of 8.70 cm and...Ch. 1 - Prob. 47PCh. 1 - Use the component method to add the vectors A and...Ch. 1 - Prob. 49PCh. 1 - Consider the three displacement vectors A=(3i3j)m,...Ch. 1 - A person going for a walk follows the path shown...Ch. 1 - Prob. 52PCh. 1 - Prob. 53PCh. 1 - Prob. 54PCh. 1 - Prob. 55PCh. 1 - The distance from the Sun to the nearest star is...Ch. 1 - Prob. 57PCh. 1 - Prob. 58PCh. 1 - Prob. 59PCh. 1 - Prob. 60PCh. 1 - Prob. 61PCh. 1 - Prob. 62PCh. 1 - Prob. 63PCh. 1 - Prob. 64PCh. 1 - A child loves to watch as you fill a transparent...Ch. 1 - One cubic centimeter of water has a mass of 1.00 ...Ch. 1 - Prob. 67PCh. 1 - Prob. 68PCh. 1 - A pirate has buried his treasure on an island with...Ch. 1 - Prob. 70PCh. 1 - Prob. 71P
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- The magnitu A (2.0i + 2.0j) m Solution You may wish to draw the vectors to conceptualize - (2.01 - 4.0) m and B = the situation. We calegorize this as a simple plug-in problem. Comparing this expression for A with the general expres- sion A A, i + A,j, we see that A= 2.0 m and A, = 2.0 m. We can fir = - 4.0 m. We obtain the resul- = 2.0 m and B Likewise, B tant vector R, using Equation 3.14: R = A + B = (2.0 + 2.0) i m + (2.0 – 4.0)f m (4.0i – 2.0j) m Your c tan %3D mean been or = 4.0 m R, = - 2.0 m the + Example 3.4 The Resultant Displacement Your A particle undergoes three consecutive displacements: the c (15i + 30j + 12k) cm, d = (23i – 14j - 5.0k) cn %3D O Cm, di %3D and dg = (-- 13i + 15j) cm. Find the components of the resultant displacement and its magnitude. %3D sion to th on Three-dinmensional displacements are more diffi- imagine than those in two dimensions, because the can be drawn on paper. For this problem, let us concep- e that you start with your pencil at the origin of…arrow_forwardGiven the displacement vectors A (2.00 -9.00j+ 5.00 k) m and B= (4.00 1 + 9.00 -4.00 k) m, find the magnitudes of the following vectors and express each in m terms of its rectangular components. (a) C-A+B IC) = 2-( atu tu (b) D-2A-B IDI m 1+ m j+ 3+ marrow_forwardGiven the displacement vectors A = (7.00 î - 2.00 j + 7.00 k) m and B = (8.00 î + 1.00 j - 8.00 k) m, find the magnitudes of the following vectors and express each in terms of its rectangular components. (a) C = A + B |C| = %3D m k) m (b) D = 2A - B DI = D k) marrow_forward
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