Find the magnitude even though direction is correct?

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SUMMARY

The discussion centers on 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 a force of 250 N east. The correct magnitude of acceleration is derived using the formula V = SQRT(X² + Y²), resulting in a magnitude of 550 N. The final acceleration is calculated by dividing this magnitude by the mass of the boat (250 kg), yielding an acceleration of 2.2 m/s².

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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:
Physics news on Phys.org
Welcome to PF. It's always good to see people who pay attention to units!

Glad things worked out :smile:
 

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