How Do You Calculate the Magnitude of a Resultant Vector from Multiple Forces?

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To calculate the magnitude of the resultant vector from multiple forces, begin by drawing a diagram that includes all vectors and their directions. Resolve each force into its components using trigonometric functions, considering angles relative to the cardinal directions. After obtaining the components, sum them up to find the total force in both the x (East-West) and y (North-South) directions. Finally, use the Pythagorean theorem to calculate the magnitude of the resultant vector from the summed components. Understanding these steps is crucial for solving similar physics problems effectively.
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Homework Statement



Find the magnitude of the resultant of the following series of vectors.

120N, North
190N, 60 degrees East of North
70N, 10 degrees East of South
150N, 45 degrees South of West

I have similar questions like these and not sure how to answer them, if anyone can help it would be greatly appreciated.
 
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Start by drawing a diagram with all the forces, draw the 4 directions and then sketch the forces.

Try resolving each of the forces.
 
Thanks for the reply, but physics is totally new to me and I've been online to try to teach myself but I'm having no luck...can you be more specific.
 
See here for more information about resolving forces.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

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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