Practice Problem: A vector N is known to start at the origin and to end at (5,-4). Ignore the units of measurement. a. Draw the vector in a Cartesian plane. b. What is the x-component ofN? c. What is the y-component ofN? d. What is the value of N i.e., the magnitude of N? Answer: 6.4031 e. Nmakes an acute angle 0 with respect to the horizontal. What is its value? Answer: 38.659g f. In which quadrant does N lie?

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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Demonstrate and solve the following:

Solution: The horizontal component is M, = -3 m. Note that it is negative since it is directed to the left.
The vertical component, on the other hand, is M, = +5 m. It is positive since it is directed upwards. Solving
for the magnitude M,
M = M? + M3
M = (-3)2 + (+5)²
M = 5.8310 m
Solving for the reference angle 6,
e = Arctan
|M,
e = Arctan
e = 59.0362°
Since the x- and y-components of M are negative and positive, respectively, applying the sign convention
for Cartesian coordinates, the vector can be located to be facing the second quadrant.
Hence, vector M is 5.8310 m, directed 59.0362° with respect to the horizontal, located in quadrant II.
Practice Problem: A vector N is known to start at the origin and to end at (5,-4). Ignore the units of
measurement.
a. Draw the vector in a Cartesian plane.
b. What is the x-component of N?
c. What is the y-component of N?
d. What is the value of N i.e., the magnitude of N?
Answer: 6.4031
e. N makes an acute angle e with respect to the horizontal. What is its value?
Answer: 38.6598°
f. In which quadrant does N lie?
Transcribed Image Text:Solution: The horizontal component is M, = -3 m. Note that it is negative since it is directed to the left. The vertical component, on the other hand, is M, = +5 m. It is positive since it is directed upwards. Solving for the magnitude M, M = M? + M3 M = (-3)2 + (+5)² M = 5.8310 m Solving for the reference angle 6, e = Arctan |M, e = Arctan e = 59.0362° Since the x- and y-components of M are negative and positive, respectively, applying the sign convention for Cartesian coordinates, the vector can be located to be facing the second quadrant. Hence, vector M is 5.8310 m, directed 59.0362° with respect to the horizontal, located in quadrant II. Practice Problem: A vector N is known to start at the origin and to end at (5,-4). Ignore the units of measurement. a. Draw the vector in a Cartesian plane. b. What is the x-component of N? c. What is the y-component of N? d. What is the value of N i.e., the magnitude of N? Answer: 6.4031 e. N makes an acute angle e with respect to the horizontal. What is its value? Answer: 38.6598° f. In which quadrant does N lie?
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