Find the magnitude even though direction is correct?

In summary, the wind exerts a force of 490 N north on a sailboat, while the water exerts a force of 250 N east. With a mass of 250 kg, the boat's acceleration can be found by taking the magnitude of the resultant force, which is calculated to be 550 N. The direction of the acceleration can be found by using the tangent inverse function and is determined to be 62.96 degrees.
  • #1
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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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  • #2
Welcome to PF. It's always good to see people who pay attention to units!

Glad things worked out :smile:
 

Related to Find the magnitude even though direction is correct?

1. What is magnitude?

Magnitude is the measure of the size or strength of an object or phenomenon. It is typically represented by a numerical value and a unit of measurement.

2. How do you find the magnitude of a vector?

The magnitude of a vector can be found by using the Pythagorean theorem, which states that the magnitude (or length) of a vector is equal to the square root of the sum of the squares of its components. In other words, if a vector has components x and y, its magnitude is equal to √(x² + y²).

3. What is the difference between magnitude and direction?

Magnitude refers to the size or strength of a vector, while direction refers to the angle at which the vector is pointing in relation to a reference frame. Both magnitude and direction are necessary to fully describe a vector.

4. Why is it important to know the magnitude of a vector even if the direction is correct?

The magnitude of a vector provides valuable information about the strength or intensity of a physical quantity. Even if the direction is correct, knowing the magnitude can help determine the total effect or impact of the vector. For example, in physics, knowing the magnitude of a force is crucial in calculating the acceleration of an object.

5. Can the magnitude of a vector be negative?

Yes, the magnitude of a vector can be negative. In physics, negative magnitudes are often used to indicate a direction opposite to the positive direction, such as in the case of displacement or velocity. However, in mathematics, magnitudes are typically represented as positive values.

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