What is the sum of the following four vectors in unit-vector notation? For that sum, what are
(b) the magnitude,
(c) the angle in degrees, and
(d) the angle in radians?
E: 6.36 m at +0.90 rad
F: 4.52 m at -75 °
G: 3.31 m at +1.20 rad
H: 5.4 m at -210 °
[[[Warning! Make a graphical solution first so you will know what quadrant your resultant lies in.]]]
(a) ______ i + ______ j
(b) magnitude = ______ m
(c) angle = ______ degrees
(d) angle = ______ radian
I will be happy to check your answers, or critique your thinking. We don't do tests for students.
it's not a test. just a hw assignment one of a bunch of questions im stuck on.
~lor
I apologize for any misunderstanding. Let's work through the problem together to find the sum of the four vectors and the requested values.
To find the sum of the given vectors in unit-vector notation, we will first convert each vector from polar form to rectangular form using trigonometric functions:
E = 6.36 m at +0.90 rad
To convert to rectangular form:
E = (6.36 * cos(0.90))i + (6.36 * sin(0.90))j
E = 5.69i + 3.91j
F = 4.52 m at -75 °
To convert to rectangular form:
F = (4.52 * cos(-75))i + (4.52 * sin(-75))j
F = 0.995i - 4.331j
G = 3.31 m at +1.20 rad
To convert to rectangular form:
G = (3.31 * cos(1.20))i + (3.31 * sin(1.20))j
G = 0.795i + 3.024j
H = 5.4 m at -210 °
To convert to rectangular form:
H = (5.4 * cos(-210))i + (5.4 * sin(-210))j
H = -4.663i - 2.739j
Now, let's add the rectangular form of the vectors together:
Sum of E, F, G, and H:
Sum = E + F + G + H
Sum = (5.69 + 0.995 + 0.795 - 4.663)i + (3.91 - 4.331 + 3.024 - 2.739)j
Sum = (2.822)i - (0.137)j
(a) The sum in unit-vector notation:
Sum = 2.822i - 0.137j
(b) To find the magnitude of the sum:
Magnitude (|Sum|) = √[(2.822)^2 + (-0.137)^2]
Magnitude = √[7.956 + 0.018]
Magnitude ≈ √7.974
Magnitude ≈ 2.82 m (rounded to two decimal places)
(c) To find the angle in degrees:
Angle = arctan(-0.137 / 2.822)
Angle ≈ -2.79° (rounded to two decimal places)
(d) To find the angle in radians:
Angle (in radians) = Angle (in degrees) * π / 180
Angle (in radians) ≈ -2.79° * π / 180
Angle (in radians) ≈ -0.0486 rad (rounded to four decimal places)
Therefore, the answers are:
(a) The sum in unit-vector notation is 2.822i - 0.137j
(b) The magnitude of the sum is approximately 2.82 m
(c) The angle of the sum is approximately -2.79°
(d) The angle of the sum is approximately -0.0486 rad