Add the following vector using the Component law. 3 N in a direction 15° south of west and 4 N in a direction 12° east of south.
Of course it's not coincidence. You've used the following names on your posts:
Joe, Eat My Shorts, Yes, Poo, Tati, Crusades , and many more.
You're lucky you weren't banned for pretending to be a tutor. After this, choose one name, like Joe, and use it on all of your posts.
15° south of west and 4 N in a direction 12° east of south.
15° south of west ----> 195° in trig notation
12° east of south ---> 282° in trig notation
Resultant = 3(cos 195°, sin195°) + 4(cos282°, sin282°)
= (-2.898,-.776) + (.832, -3.913)
= ( -2.066, -4.689) <----- your required answer, same as Damon's answer
|R| = √((-2.066)^2 + (-4.689)^2 )
= 5.124
My calculator has enough memory locations to store each of
the answers, which I did.
Lol F this Niiiiiiiiiggga
East (x) = Fx = 4 sin 12 - 3 cos 15
North (y) = Fy = -4 cos 12 - 3 sin 15
|F| = sqrt (Fx^2+Fy^2)
tan angle below -x axis= Fy/Fx (assuming both Fx and Fy are negative, Quadrant III)
Our identical names are coincidence.
Coincidence? I think not.
Pretending to be a tutor, the shame
Ikr XD
To add the given vectors using the Component law, we need to break down each vector into its x-component and y-component and then add them separately.
Let's break down each vector:
Vector 1: 3 N in a direction 15° south of west
- The magnitude of the vector is 3 N.
- The angle with respect to the x-axis is (180° - 15°) = 165°
- To find the x-component, we can use cosine of the angle: x1 = 3 N * cos(165°)
- To find the y-component, we can use sine of the angle: y1 = 3 N * sin(165°)
Vector 2: 4 N in a direction 12° east of south
- The magnitude of the vector is 4 N.
- The angle with respect to the x-axis is (270° + 12°) = 282°
- To find the x-component, we can use cosine of the angle: x2 = 4 N * cos(282°)
- To find the y-component, we can use sine of the angle: y2 = 4 N * sin(282°)
Now, let's calculate the x and y components:
x1 = 3 N * cos(165°) = -2.96 N (rounded to two decimal places)
y1 = 3 N * sin(165°) = -0.73 N (rounded to two decimal places)
x2 = 4 N * cos(282°) = 1.97 N (rounded to two decimal places)
y2 = 4 N * sin(282°) = -3.88 N (rounded to two decimal places)
Finally, to add the vectors, we simply add the x-components and y-components separately:
x_total = x1 + x2 = -2.96 N + 1.97 N = -0.99 N (rounded to two decimal places)
y_total = y1 + y2 = -0.73 N - 3.88 N = -4.61 N (rounded to two decimal places)
The resulting vector is approximately -0.99 N in the x-direction and -4.61 N in the y-direction.