Finding the magnitude of velocity given vx and vy

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To find the magnitude of velocity given the components vx and vy, use vector addition based on Pythagorean theorem. The equation v² = vx² + vy² allows for calculating the hypotenuse of a right triangle formed by the velocity components. The discussion clarifies that this problem does not require calculus, as it involves basic vector addition. The participant initially misunderstood the question but confirmed their understanding after receiving guidance. This approach effectively resolves the query regarding calculating velocity magnitude.
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Homework Statement


I am working on a lab, and I have come up with graphs (and the data set) for vy vs. time and vx vs. time, but I'm not sure how to determine v? I just need to come up with the equation so solve for v, but we haven't done anything calc oriented in the course yet.


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The Attempt at a Solution

 
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It has nothing to do with calculus, just simple vector addition. The horizontal component of v is vx while the vertical component of v is vy. Hence, by Pythagora's theorem, we have v^{2} = v_{x}^{2} + v_{y}^{2}
 
Have you seen vectors? There is a right triangle with vx as one right side and vy as the other. You are looking for the speed v which is the hypotenuse of the triangle. So ...
 
Okay thank you both for your help.
I guess I just misunderstood the question, we have covered adding vectors in the course so I am able to do that.

thanks again!
 
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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