Respuesta :
Answer:
Explanation:
a)Magnitude = [tex]\sqrt{(x1-y2)^{2} + (x1-x2)^{2} }[/tex]
84=[tex]\sqrt{(0- (-67))^{2} + (x-0)^{2} }[/tex]
x= +50.67 or -50.67 units
b) We are given that the resultant is entirely in the -ve x direction which means that the y-component of the resultant is 0; It means that the y-component of the next vector = -ve of the y component of the initial vector i.e 67.
To make the magnitude 80 units in the negative x direction where the y component is 0, the x component must be -130.67(-50.67 - 80) as the x component is + 50.67units.
Magnitude = [tex]\sqrt{(0- (67))^{2} + (-130.67)^{2} }[/tex] = 146.85 units
c) The direction vector = 67/146.85 i - 130.67/146.85 j where i corresponds to the vector in y direction and j corresponds to the vector in x direction. Or this vector is at an angle of 180 - [tex]Tan^{-1}(67/130.67)degrees[/tex] i.e 152.85 degrees from the +ve x-axis.
A) The two possibilities for the x-component are; +50.67 units or -50.67 units
B) The magnitude of the vector added to the original one is; 146.85 units
C) The direction of the vector is; θ = 207.15°
A) We are given;
Magnitude of vector = 84 units
Y-component of the vector = -67 units
We know that the formula for for 2 vectors like this in x and y direction is;
A = xi^ + yj^
Where A is the magnitude of the resultant
x is the value of the x-component
y is the value of the y-component
Thus;
A = √(x² + y²)
84 = √(x² + (-67)²)
84² = x² + 4489
7056 = x² + 4489
x = ±√(7056 - 4489)
x = ±50.67 units
B) From A above, let us take the positive value of the x-component and as such our original vector will be;
A = 50.67i^ - 67j^
We want to add another vector to this that would make the resultant to be -80 units in the x direction. Thus, A = -80i and if the new additional vector is V^, then we have;
-80i^ = (50.67i^ - 67j^) + V^
V^ = -(80 + 50.67)i^ + 67j^
V = -130.67i^ + 67j^
The magnitude of vector V is;
V = √(x² + y²)
V = √(-130.67)² + 67²)
V = 146.85 units
C) The direction of the vector V is;
θ = tan^(-1) (y/x)
θ = tan^(-1) (67/-130.67)
θ = -27.15°
Since it points entirely in the negative x axis, then the angle is;
180 - (-27.15) = 207.15°
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