University Physics Volume 1
18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: OpenStax - Rice University
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Textbook Question
Chapter 2, Problem 1CQ
Scalars and Vectors
A weather forecast states the temperature is predicted to be
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1. Draw and label the vector with these components. Then determine the magnitude and
angle of the vector.
a- A, = 3 ,A, = -2
b- By = -2 ,B, = 2
2. What is the speed of horse in meter per second that runs a distance of 1.2 miles in 2.4
minutes?
3. A car moving along X- axis according on the function:
X (t) = 2 t2 + 5 t + 7 on [1,2] Find:
a- The average velocity.
b- The acceleration at 3s.
4. Julie is walking around a track at a 2m/s for some exercise. She then decides to start
jogging so she accelerates at a rate of 0.5m/s for 3 seconds.
How far did Julie travel from the time she started to accelerate to the end of the 3 seconds?
5. Ralph uses a 2000 N force to push his car along a road for 1000 m. It takes him500 s
to do this
a- Calculate the amount of work that Ralph did on the car.
b- Calculate the amount of power that he generated.
The Scalar Product
The vectors A andB are given by A = 31 + 1j and B = -1î + 1j.
(a) Determine the scalar product A - B.
SOLUTION
Conceptualize There is no physical system to imagine here. Rather, it is purely a mathematical exercise involving two (vectors
Categorize Because we have a definition for the scalar product, we categorize this example as a substitution vy problem.
Substitute the specific vector expressions for A and B:
A-B = (31 + 1j) - (-1î + 1j)
= [3i - (-1)i - [31 - 15 - 13 - (-1) + [1j - 15]
The same result is obtained when we use the equation A -B = AB, + A8, + A,B, directly, where A, = 3, A, = 1, B, = -1 and 8, = 1.
(b) Find the angle e between A and B.
SOLUTION
Evaluate the magnitudes of A and B using the Pythagorean theorem:
A = VA,? + A, =
B = V82 + B 2 =
Use the equation A - B = AB cos(e) and the result from part (a) to find the angle (in degrees).
cos(e) =
AB
EXERCISE
As a particle moves from the origin to (7i + 5j) m, it is acted upon by a force given by (7î +…
1. If the force vector shown below has x, y, andz
components of 300 N, 400 N and 800 N,
respectively,
a. Write it in vector form
I.
b. Then determine the scalar component of the
force in the direction defined by, u=
0.250i+ 0.968j
Chapter 2 Solutions
University Physics Volume 1
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(b) If AF=BF...Ch. 2 - You fly 32.0 km in a straight line in still air in...Ch. 2 - Rectangular coordinates of a point are given by...Ch. 2 - If the polar coordinates of a point are (r,)and...Ch. 2 - Prob. 74APCh. 2 - Starting at the island of Moi in an unknown...Ch. 2 - An air traffic controller notices two signals from...Ch. 2 - Show that when A+B=C then A2+B2+2ABcos , where is...Ch. 2 - Four force vectors each have the same magnitude...Ch. 2 - A skater glides along a circular path of radius...Ch. 2 - A stubborn dog is being walked on a leash by its...Ch. 2 - If the velocity vector of a polar bear is u=(-18.0...Ch. 2 - Find the scalar components of three-dimensional...Ch. 2 - A diver explores a shallow reef off the coast of...Ch. 2 - A force vector A has x and y components,...Ch. 2 - Vectors A and B are two orthogonal vectors in the...Ch. 2 - For the three-dimensional vectors in the following...Ch. 2 - Show that (BC)A is the volume of the...Ch. 2 - Vector B is 5.0 cm long and vector A is 4.0 cm...Ch. 2 - What is the component of the force vector G=(3.0...Ch. 2 - The following figure shows a triangle formed by...Ch. 2 - between points in a plane do not change when a...
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