Grade 11 · Science · Physics

11th grade Add vectors and split them into parts worksheet

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Add vectors and split them into parts

Grade 11 Science Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Ari pulls a cart's handle with 10 N at 60° above the ground. What is the horizontal part of the pull, to the nearest 0.1 N?
Bo pulls a cart's handle with 20 N at 30° above the ground. What is the horizontal part of the pull, to the nearest 0.1 N?
Esme pulls a cart's handle with 40 N at 37° above the ground. What is the horizontal part of the pull, to the nearest 0.1 N?
4.
In the arrow grid, what are the components of arrow F, Jun?
- 8 N along x, 6 N along y
- 6 N along x, 8 N along y
- 14 N together
- 10 N along x, 0 along y
5.
In the arrow grid, what is the magnitude of arrow F, Kira?
Use the picture in question 4.
- 10 N
- 2 N
- 14 N
- 48 N
6.
In the arrow grid, what is tan θ for arrow F's angle above the x-axis, Luz?
Use the picture in question 4.
- 8 ÷ 6
- 6 ÷ 8 = 0.75
- 6 ÷ 10
- 10 ÷ 8
7.
A = (3, 4) N and B = (5, −1) N. What is A + B, Milo?
- (8, 3) N
- (8, 5) N
- (2, 5) N
- (15, −4) N
8.
A = (6, 2) m and B = (−6, 3) m. What is A + B, Noah?
- (0, 1) m
- (0, 5) m
- (12, 5) m
- (−36, 6) m
9.
A boat points straight across a river while the current flows downstream. Where does it land, Ren?
- Upstream of the point straight across
- Back where it started
- Downstream of the point straight across
- At the point straight across
10.
A boat points straight across a river. Does a faster current change the crossing time, Tala?
- No; only the across-speed sets it
- Yes; a faster current makes it shorter
- Yes; a faster current makes it longer
- Yes; the boat must fight the current

11th grade Add vectors and split them into parts worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Add vectors and split them into parts. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can add vectors tip to tail. I can find the size of a right-angle sum with the Pythagorean theorem and its direction with tan θ.
I can split a vector into components, x = F cos θ and y = F sin θ (angle from +x), and read components off a grid.
I can add vectors by components, keeping signs.
I can work through a boat crossing a river or a drone in the wind. I can find the drift, the speed over the ground and the heading needed to land straight across.

Standard: supports HS-PS2-1

Words to know

resultant: The single vector that equals two or more vectors added

tip to tail: Start the next arrow where the last one ends

component: The part of a vector along x or along y

magnitude: A vector's size: √(x² + y²)

heading: The direction a boat or drone points

Common mistakes

Your child added the sizes of two vectors at an angle. Vectors at right angles combine by the Pythagorean theorem, not by adding.

Your child swapped sine and cosine. With the angle measured from the x-axis, the x-part uses cosine and the y-part uses sine.

Your child swapped the x and y parts. x runs across (east), y runs up (north); read each from its own axis.

Questions parents ask

What is the most common mistake with add vectors and split them into parts?

Your child added the sizes of two vectors at an angle. Vectors at right angles combine by the Pythagorean theorem, not by adding.

Are these 11th grade science worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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