Solving Vector Problem B: Find Magnitude & Direction

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In summary, the problem involves a ship sailing east across a lake at 19 mi/hr and encountering a current flowing north at 3.00 mi/hr. The resultant velocity is found to be 19 mi/hr and the direction is 8.97 degrees north of east. The resultant velocity can also be calculated by subtracting the two given velocities as vectors, resulting in a velocity of <3, 19>.
  • #1
cowgiljl
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A ship sails due east across lake at 19 mi/hr. The ship encounters a current flowing due northat 3.00 mi/hr

A calculate the resultant velocity ( be sure to calculate the magnitude and direction)

I drew a picture

R^2 = 19^2 + 3^2
R = about 19 mi/hr



B) In what direction should the ship head in order to offswet the effect of the current
tan-1 (3/19) = 8.97 degrees n of east

Just need some reassurance I am doing these right
 
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  • #2
First of all write vector eqn in terms of i,j,k components

then apply
[tex]V_a_b = V_a - V_b[/tex]

rel velocity of a wrt b= vel of a - vel of b
 
  • #3
Always try to write vector eqn if you are not able understand graphically and derive the results accordingly
 
  • #4
Two points:

1) The problem said "calculate the resultant velocity " NOT "speed".
Technically, velocity is a vector quantity.
2) The problem specifically said " be sure to calculate the magnitude and direction"

You have only given the resultant speed (magnitude of the velocity).

You should either find the angle (arctan(3/19) north of east) or
(much simpler) write the two given velocities as vectors and add:
Using the standard convention that <1, 0> is east, <0, 1> north,
19 m/h n is <0, 19> and 3 m/h e is <3, 0>

The resultant velocity is <3, 19>. That was easy!
 

FAQ: Solving Vector Problem B: Find Magnitude & Direction

What is a vector and how is it different from a scalar?

A vector is a mathematical quantity that has both magnitude and direction, while a scalar only has magnitude. This means that a vector represents a physical quantity with both size and direction, while a scalar only represents size.

How do I find the magnitude of a vector?

The magnitude of a vector can be found using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the vector's components. Alternatively, you can also use the magnitude equation, which is the square root of the dot product of the vector with itself.

How do I find the direction of a vector?

The direction of a vector can be found using the inverse tangent function, where the direction is equal to the ratio of the vector's y-component to its x-component. This will give you the angle in radians, which can then be converted to degrees if needed.

Can I use a calculator to solve vector problems?

Yes, most scientific and graphing calculators have built-in functions for solving vector problems, such as finding the magnitude and direction. However, it is still important to understand the concepts behind these calculations.

How can I check if my answer for a vector problem is correct?

You can check your answer by using the Pythagorean theorem to find the magnitude and comparing it to your calculated magnitude, and by using trigonometric functions to check the direction. Additionally, you can use vector addition and subtraction to see if your answer is consistent with other known vectors in the problem.

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