Find the magnitude even though direction is correct?

AI Thread Summary
The discussion revolves around calculating the acceleration of a sailboat subjected to wind and water forces. The wind exerts a force of 490 N north, while the water exerts 250 N east, leading to a resultant force vector. The user initially calculated the magnitude of the resultant force incorrectly as 550 Kg m/s², confusing it with the force rather than acceleration. After realizing the mistake, they correctly divided the resultant force by the boat's mass to find the acceleration. The conversation highlights the importance of unit consistency in physics calculations.
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Homework Statement



The force exerted by the wind on the sails of a sailboat is 490 N north. The water exerts a force of 250 N east. If the boat (including its crew) has a mass of 250 kg, what are the magnitude and direction of its acceleration?

Homework Equations



V= SQRT(X2+Y2)
Tan-1(Vy/Vx)

The Attempt at a Solution



Drew it out on a piece of paper:
(0, 490N)
(250, 0)
So: (250, 490)

Direction = tan-1(490/250) = 62.96Magnitude = V = SQRT(490^2+250^2) = 550 = Wrong?
Why would the magnitude be incorrect? Or can anyone point out where I may be wrong?
Thank you!Edit - The answers are supposed to be in acceleration (m/s^2) and my magnitude came out to be:

550 Kg m/s^2 so I just divided by the kg and got my answer!
Silly mistake ;)
 
Last edited:
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Welcome to PF. It's always good to see people who pay attention to units!

Glad things worked out :smile:
 

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