2 vectors act on a bolt. vector 1(1200/70 degrees) vector 2(900/205 degrees) then E = ? must show work!
V1 + V2 = 1200[70o] + 900[205o]
X = 1200*cos70 + 900*cos205 = -405.3
Y = 1200*sin70 + 900*sin205 = 747.3
tanAr = Y/X = 747,3/-405.3 = -1.84376
Ar = -61.53o = Reference angle.
A = -61.53 + 180 = 118.5o
Vr = Y/sinA = 747.3/sin118.5 = 850.3[118.5o] = Resultant vector.
To find the resultant vector E, we need to add the individual components of vectors 1 and 2. The components can be determined using trigonometry, where the magnitude of a vector is multiplied by the cosine of its angle to get the horizontal component, and by the sine of its angle to get the vertical component.
Let's break down the given information:
Vector 1: magnitude = 1200, angle = 70 degrees
Vector 2: magnitude = 900, angle = 205 degrees
Step 1: Convert the angles from degrees to radians
To use trigonometric functions, we need to convert the angles from degrees to radians. The conversion can be done by multiplying the degree value by π/180.
Angle of vector 1 in radians = 70 * π/180 radians
Angle of vector 2 in radians = 205 * π/180 radians
Step 2: Calculate the horizontal and vertical components of vector 1
Horizontal component of vector 1 = magnitude of vector 1 * cos(angle of vector 1 in radians)
Vertical component of vector 1 = magnitude of vector 1 * sin(angle of vector 1 in radians)
Horizontal component of vector 1 = 1200 * cos(70 * π/180)
Vertical component of vector 1 = 1200 * sin(70 * π/180)
Step 3: Calculate the horizontal and vertical components of vector 2
Horizontal component of vector 2 = magnitude of vector 2 * cos(angle of vector 2 in radians)
Vertical component of vector 2 = magnitude of vector 2 * sin(angle of vector 2 in radians)
Horizontal component of vector 2 = 900 * cos(205 * π/180)
Vertical component of vector 2 = 900 * sin(205 * π/180)
Step 4: Find the sum of the horizontal and vertical components
To get the horizontal component of the resultant vector E, add the horizontal components of vectors 1 and 2.
To get the vertical component of the resultant vector E, add the vertical components of vectors 1 and 2.
Horizontal component of E = Horizontal component of vector 1 + Horizontal component of vector 2
Vertical component of E = Vertical component of vector 1 + Vertical component of vector 2
Finally, find the magnitude and angle of vector E using the sum of the horizontal and vertical components.
Magnitude of E = √(Horizontal component of E)^2 + (Vertical component of E)^2
Angle of E = arctan(Vertical component of E / Horizontal component of E)
By following these steps and plugging in the values given, you should be able to calculate the magnitude and angle of vector E.