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 - Challenge Me

NameDate

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

A boat crosses a river 60 m wide, pointing straight across at 3 m/s. The current flows at 2 m/s. How far downstream does it land, Ari?
A boat crosses a river 90 m wide, pointing straight across at 3 m/s. The current flows at 1 m/s. How far downstream does it land, Bo?
A boat crosses a river 48 m wide, pointing straight across at 4 m/s. The current flows at 2 m/s. How far downstream does it land, Esme?
4.
In the arrow grid, what is the size of the net force on the cart, Jun?
- 50 N
- 10 N
- 70 N
- 25 N
5.
In the arrow grid, about what angle north of east does the net force point, Kira?
Use the picture in question 4.
- About 53°
- About 90°
- About 45°
- About 37°
6.
In the arrow grid, what single extra force would keep the cart from moving, Luz?
Use the picture in question 4.
- 50 N, 53° north of east
- 50 N, 53° south of west
- 70 N, 53° south of west
- 50 N, 37° south of west
7.
Milo says two 10 N forces always add to 20 N. Agree or disagree?
- Disagree: it depends on the angle
- Agree: angles don't change a sum
- Agree: forces just add
- Agree: the x-part is F sin θ
8.
To land at the point straight across a river, which way should a boat point, Ren?
- Straight across
- Angled downstream
- Angled upstream
- Straight upstream
9.
A boat crosses at 4 m/s for 20 s while a 3 m/s current flows. How far downstream does it drift, Tala?
- 100 m
- 60 m
- 0 m
- 80 m
10.
A drone flies 12 m/s north in a 5 m/s wind blowing east. What is its speed over the ground, Zee?
- 13 m/s
- 17 m/s
- 12 m/s
- 7 m/s

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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