Physics: Vector Help - Magnitude & Angle Calculations

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To find the equilibrant vector of a resultant vector measuring 5 units at an angle of 23 degrees, it is necessary to determine that the equilibrant has the same magnitude but an angle of 203 degrees, as it is opposite in direction. For the vector with a magnitude of 8.73 units at an angle of 155 degrees, the x-component is calculated using the formula F*cos(x) and the y-component using F*sin(x). The confusion surrounding counter-clockwise angles is clarified: counter-clockwise angles are considered positive while clockwise angles are negative. Understanding these conventions is crucial for accurately calculating vector components and magnitudes. Proper application of these principles will lead to correct vector analysis.
buffgilville
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Can someone please help me with this?
1) A resultant vector is 5 units long and makes an angle of 23 degrees measured counter-clockwise with respect to the positive x-axis. What are the magnitude and angle (measured counter-clockwise with respect to the positive x-axis) of the equilibrant vector?

2) Find the x- and y-components of the vector whose magnitude is 8.73 units making an angle of 155 degrees measured counter-clockwise with respect to the positive x-axis.
 
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These kinds of questions have already been answered, look at some other posts.

Think of the fact that the x-component of a vector of magnitude F and angle x with the x-axis is
equal to F*cos (x). The y-component is F*sin(x)

Once the components are given you can work the other way around and determin the magnitude of the vector as F = sqrt(x² + y²)

regards
marlon
 
But what does the counter-clockwise mean? Does it mean that the angle is negative? I'm confused.
 
Last edited:
Clockwise means a negative angle, and counter-clockwise means a positive angle.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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