2D Non Projectile Motion

Learn how to do 2D non-projectile motion problems. Non projectile motion just means that the object is not in the air in freefall.

Head to Tail

It is important to draw vectors head to tail just like when following directions. To go to the mall you would not go back to the origin (beginning) before the next direction.  The end of the last direction has an arrow tip head.  The head of the last direction is where the tail of the new instruction begins every time.

Head to Tail Vectors

Minimum and Maximum

When vectors are in the same plane, i.e. only X axis, the minimum displacement will be when they are in opposite directions.  When vectors are facing the same direction the displacements add up.  Pythagorean Theorem and Trigonometry functions SOH CAH TOA are used when vectors are not on the same plane.  The rest of this page will show you how to do this.

 

Maximum and Minimum Adding Vectors

Either Vector First

When adding two vectors, 20 meters north and 40 meters east, you would start with an origin dot then draw them head to tail.  It does no matter which one you draw first as long as they are head to tail.   The magnitude will be the same either direction you follow first but you'll have complimentary angles and descriptions.  One may be 27° N of E and the other would be 63° E of N.  Complimentary means the two add up to 90°.

Same Resultant

Describing The Direction

Directions have a baseline, starting direction from which the angle is directed, described many possible ways.

  • From the +X axis
  • East
  • Right
  • And Many Others

Look at the context of the problem to determine which to use.

The angle will be directed from that baseline and needs a direction as well.  Look at the difference between 20° N of E and 20° N of W.  Both are 20° north but without the baseline the direction is uncertain.  Of east or of west is a baseline that completes the direction.

 

Angle Description

Determining Components of a Vector

What is the east component of 85 m 20° North of East?

When you have a question like this you are trying to find a component of a vector.  Because of being at an angle north of east, this vector will have a north component and east component that make it up.  Follow the directions to solve for the east component of this vector.

  1. Draw an origin dot
  2. From the origin draw the last direction you see, east in this description (85m 20° North of East).  Be sure to include the arrow tip.  This represents your east component.
  3. Continue head to tail, draw the second to last direction, north in this description (85m 20° North of East).  Also include an arrow tip.  This represents your north component.
  4. Next draw the resultant, our hypotenuse.  Go back to the origin and draw the arrow from start to finish.  This represents the original vector described.
  5. Now place the 20° angle closest to the origin dot (85m 20° North of East)
  6. Lastly place the magnitude, 85m, on the hypotenuse.
Drawing A 2D Vector

Now that you drew the vector, you have three arrows, one on the hypotenuse, one east, and one north.  The north and east arrow represent components.  We are asked to solve for the east, so we will use our trig functions to figure out that side.  The arrow in red is facing east and what we are solving for.  We have the 85 m hypotenuse, a 20° angle, and the adjacent side as our unknown.  This leads us to the cosine function which rearranges to adj = (cos Ө)(hyp).

adj = (cos Ө)(hyp)

adj = (cos 20)(85) = 80 m

The final answer to the question rounds to 35 meters east.

East Component

Adding Two Vectors on Different Axis

What is the resultant of a horse that travels 45 meters north followed by 75 meters west?

When you see a question that has two separate vectors, 45 meters north, and 75 meters west, you are adding vectors.  When adding two vectors on different axis, you can't simply add or subtract.  Follow the following step as we go through an example to get the three part resultant answer.  The answer will have a magnitude, an angle, and a description of that angle.

Adding 45m North to 75m West
Adding two vectors, 45m north and 75m west, to get the resultant
  1. Draw an origin dot
  2. Draw the first component (45 meters north) and label it
  3. Draw the next component (75 meters west) and label it starting at the previous arrow tip
  4. Go back to the origin and draw the resultant from beginning to where the components ended (See the blue line above).
  5. Use the Pythagorean Theorem to determine the hypotenuse.
  6. Use inverse tangent to figure out the angle.
  7. Describe the angle ____ of ____.  The last direction is the baseline (line coming out of the origin dot) so W of N.
Vector Math and Description

Example Problems

How do you describe this vector?

100 m 40 degrees

100 m 40 degrees south of west
(Click on the picture to enlarge it)

2. What is the west component of 67.2 m/s 22° north of west?

2D Question 2
(Click on the picture to enlarge it)

3. What is the resultant of 40 meters east and 22 meters south?

2D Question 3
(Click on the picture to enlarge it)

  • To determine the magnitude of the hypotenuse you use the Pythagorean Theorem as seen above.
  • To determine the angle with an opposite and adjacent we use the inverse tangent function as seen above.
  • When describing the angle it will be from the baseline direction "of North"

The final answer here is 87 m 59° W of N.  The magnitude is 87 m, the angle is 59°, and the description is to the west of north.

2D Non Projectile Motion Quiz

2D Non Projectile Motion Quiz

30 m/s 20 degrees west of north

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Vector A and B

What is true about vector A and B as you see them above?

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Vector A and B

What is the maximum magnitude of vector A and B in any arrangement?

3 / 17

Vector A and B

What is the minimum magnitude of vector A and B in any arrangement?

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4 and 10 M Vector

What is the minimum magnitude of vector A and B in any arrangement?

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4 and 10 M Vector

What is the maximum magnitude of vector A and B in any arrangement?

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20 degrees

How would you describe the direction above?

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35 degrees

How would you describe the direction above?

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35 degrees

What is the east component of the vector above?

What is the east component of the vector above?

9 / 17

20 degrees west of north

What is the west component of 30 meters per second at 20 degrees to the west of north?

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What is the magnitude of the resultant of 50 meters north and 72 meters west?

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What is the direction of the resultant of 50 meters north and 72 meters west?

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A vector includes

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50 meters is a

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A scalar includes

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North is a

16 / 17

20 degrees north is a

17 / 17

An object starts at the origin and travels 3 m east. What must the object do next to for the displacement for be 5 m in a northeastern direction?

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