Vectors given the resultant and angle

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To solve for the resultant of two velocities given their angles, first determine the third angle of the triangle formed by the two vectors. Utilize trigonometric formulas to resolve the components of each vector. The sum of the two velocities is 7 m/s, with angles θ1 at 29.8° and θ2 at 18.3°. By applying the sine and cosine rules, the remaining side can be calculated. Understanding these principles is essential for accurately calculating vector sums in physics.
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Homework Statement


The figure depicts the sum of two velocities, vA and vB. The value of the sum is7 m/s and the angles shown in the image are θ1 = 29.8°, and θ2 = 18.3°.
q1104jzu.bxc.png


Homework Equations

The Attempt at a Solution


I have no idea where to even begin on this
 
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You have two angles of the triangle, right? You can find the third angle. Then you can use some well-known trig formulas to find the remaining side.
 
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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