Explanation It is given that the components of A → satisfy the relation given below. A x = − A y ≠ 0 From the obove equation, it can be concluded that the components of A → are equal in magnitude but unequal in direction. Formula to calculate the possible directions of vector A → is, θ = tan − 1 ( A y A x ) (1) Here, θ is the direction of vector A → . A x is the component of vector A → in x direction. A y is the component of vector A → in y direction. Consider the vector diagram for the given vector components when A x < 0 . Figure (1) When A x < 0 , the value of component of vector A → in x direction is, A x = − a When A x < 0 , the value of component of vector A → in y direction is, A y = a Substitute ( − a ) for A x and a for A y in equation (1). θ = tan − 1 ( ( + a ) ( − a ) ) = tan − 1 ( − 1 ) = − 45 ° Solve the further equation. θ = 180 ° + ( − 45 ° ) = 135 ° Thus, the possible direction of vector A → when A x < 0 is 135 ° counterclockwise from the x-axis

5th Edition

ISBN: 9780321976444

Author: James S. Walker

Publisher: PEARSON

See similar textbooks

Question

Chapter 3, Problem 11CQ

To determine

The possible directions of vector A→ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 10CQ

Chapter 3, Problem 12CQ

Students have asked these similar questions

Two vectors, a and b, have magnitudes 4m and 5m, respectively. Vector c= (a+ b). Considering all possible orientations of a and b, what is: 1) the maximum possible magnitude for c 2) the minimum possible magnitude for c?

Given vector A = xz ax -xy ay +yz az Transform A into cylindrical coordinate and it's magnitude at point (1,30o,2) is equal to:

The magnitudes of two vectors A → a n d B → are 12 units and 8 units, respectively. What are the largest and smallest possible values for the resultant vector R → = A → + B →?

Chapter 3 Solutions

Physics (5th Edition)

Ch. 3.1 - Is it possible for two vectors to be different...Ch. 3.2 - A vector has the components Ax = 5 m and Ay = 3 m....Ch. 3.3 - Several vectors are shown in Figure 3-16. The red...Ch. 3.4 - Which of the vectors shown in Figure 3-20 has the...Ch. 3.5 - An object moves along the brown path in Figure...Ch. 3.6 - Suppose the speed of the boat is increased in part...Ch. 3 - For the following quantities, indicate which is a...Ch. 3 - Which, if any of the vectors shown in Figure 3-36...Ch. 3 - Given that A+B=0, (a) how does the magnitude of B...Ch. 3 - Can a component of a vector be greater than the...

Ch. 3 - Prob. 5CQ Ch. 3 - Can a vector with zero magnitude heve one or more...Ch. 3 - Prob. 7CQ Ch. 3 - Prob. 8CQ Ch. 3 - Prob. 9CQ Ch. 3 - Prob. 10CQ Ch. 3 - Prob. 11CQ Ch. 3 - Use a sketch to show that two vectors of unequal...Ch. 3 - Rain is falling vertically downward and you are...Ch. 3 - When sailing, the wind feels stronger when you...Ch. 3 - Suppose that each component ot a certain vector is...Ch. 3 - Rank the vectors in Figure 3-37 in order of...Ch. 3 - Rank the vectors in Figure 3-37 in order of...Ch. 3 - Rank the vectors in Figure 3-37 in order of...Ch. 3 - The press box at a baseball park is 44.5 ft above...Ch. 3 - You are driving up a long, inclined road. After...Ch. 3 - A One-Percent Grade A road that rises 1 ft for...Ch. 3 - You walk in a straight line tor 95 m at an angle...Ch. 3 - Find the x and y components of a position vector r...Ch. 3 - A vector has the components Az = 22 m and Ay = 13...Ch. 3 - A vector has the components Az = 36 m and Ay = 43...Ch. 3 - A baseball diamond (Figure 3-38) is a square with...Ch. 3 - A lighthouse that rises 49 ft above the surface of...Ch. 3 - H2O A water molecule is shown schematically in...Ch. 3 - Prob. 15PCE Ch. 3 - You drive a car 660 ft to the east, then 340 ft to...Ch. 3 - Vector A has a magnitude of 50 units and points in...Ch. 3 - A treasure map directs you to start at a palm tree...Ch. 3 - A whale comes to the surface to breathe and then...Ch. 3 - Consider the vectors A and B shown in Figure 3-42....Ch. 3 - Refer to Figure 3-42 for the following questions...Ch. 3 - A vector A has a magnitude of 40.0 m and points in...Ch. 3 - An air traffic controller observes two airplanes...Ch. 3 - The initial velocity of a car, vi, is 45 km/h in...Ch. 3 - Vector A points in the positive x direction and...Ch. 3 - Vector A points in the negative x direction and...Ch. 3 - Vector A points in the negative y direction and...Ch. 3 - A basketball player runs down the court, following...Ch. 3 - A particle undergoes a displacement r of magnitude...Ch. 3 - A vector has a magnitude of 3.50 m and points in a...Ch. 3 - A vector A has a length of 6.1 m and points in the...Ch. 3 - The vector 5 2 A has a magnitude of 34 m and...Ch. 3 - Find the direction and magnitude of the vectors....Ch. 3 - Find the direction and magnitude of the vectors....Ch. 3 - For the vectors given in Problem 34, express (a)...Ch. 3 - Express each of the vectors in Figure 3-44 in unit...Ch. 3 - Referring to the vectors in Figure 3-44, express...Ch. 3 - The blue curves shown in Figure 3-45 display the...Ch. 3 - What are the direction and magnitude of your total...Ch. 3 - Predict/Calculate Moving the Knight Two of the...Ch. 3 - To visit your favorite ice cream shop, you must...Ch. 3 - Referring to Problem 41, suppose you lake 44 s to...Ch. 3 - You drive a car 1500 ft to the east, then 2500 ft...Ch. 3 - Predict/Calculate A jogger runs with a speed of...Ch. 3 - You throw a ball upward with an initial speed of...Ch. 3 - Consider a skateboarder who starts from rest at...Ch. 3 - In a soccer game a midfielder kicks the ball from...Ch. 3 - The accompanying photo shows a KC-10A Extender...Ch. 3 - As an airplane taxied on the runway with a speed...Ch. 3 - Referring to part (a) of Example 3-11, find the...Ch. 3 - A police car travels at 38.0 m/s due east while in...Ch. 3 - Consider the river crossing problem in Example...Ch. 3 - As you hurry to catch your flight at the local...Ch. 3 - In Problem 53, how much lime would it take you to...Ch. 3 - Predict/Calculate The pilot of an airplane wishes...Ch. 3 - A passenger walks from one side of a ferry to the...Ch. 3 - You are riding on a Jet Ski at an angle of 35...Ch. 3 - Predict/Calculate In Problem 57, suppose the Jet...Ch. 3 - Predict/Calculate Two people take identical Jet...Ch. 3 - CE Predict/Explain Consider the vectors A=(1.2m)x...Ch. 3 - CE Predict/Explain Two vectors are defined as...Ch. 3 - To be compliant with regulations the inclination...Ch. 3 - Find the direction and magnitude of the vector...Ch. 3 - Prob. 64GP Ch. 3 - Prob. 65GP Ch. 3 - Prob. 66GP Ch. 3 - You pilot an airplane with the intent to fly 392...Ch. 3 - Find the x, y, and z components of the vector A...Ch. 3 - Observer 1 rides in a car and drops a ball from...Ch. 3 - A person riding in a subway train drops a ball...Ch. 3 - A football is thrown horizontally with an initial...Ch. 3 - As a function of time, the velocity of the...Ch. 3 - Two airplanes taxi as they approach the terminal....Ch. 3 - A shopper at the supermarket follows the path...Ch. 3 - BIO A food particle from your breakfast takes a...Ch. 3 - Initially a particle is moving at 4.10 m/s at an...Ch. 3 - A passenger on a stopped bus notices that rain is...Ch. 3 - Predict/Calculate Suppose we orient the x axis of...Ch. 3 - Predict/Calculate The Longitude Problem In 1759,...Ch. 3 - Referring to Example 3-11, (a) what heading must...Ch. 3 - Vector A points in the negative x direction....Ch. 3 - As two boats approach the marina, the velocity of...Ch. 3 - BIO Motion Camouflage in Dragonflies Dragonflies,...Ch. 3 - BIO Motion Camouflage in Dragonflies Dragonflies,...Ch. 3 - BIO Motion Camouflage in Dragonflies Dragonflies,...Ch. 3 - BIO Motion Camouflage in Dragonflies Dragonflies,...Ch. 3 - BIO Motion Camouflage in Dragonflies Dragonflies,...Ch. 3 - BIO Motion Camouflage in Dragonflies Dragonflies,...

Knowledge Booster

The possible directions of vector A → .

Solution Summary: The author calculates the possible directions of vector stackreltoA by using the obove equation.

The possible directions of vector A→ .

Want to see the full answer?

Chapter 3 Solutions