# Worksheet: Scale Diagrams

In this worksheet, we will practice using scale diagrams to represent the resultants of combined vector quantities and the components of vectors.

**Q1: **

Some vectors are drawn to scale on a square grid. Which color vector shows the resultant of the black vectors and ?

- ABlue
- BGreen
- CRed
- DOrange

**Q3: **

The forces acting on an object are represented by blue and green vectors that are drawn to scale on a square grid. The red vector is the resultant of the green vector and the blue vector. What is the angle between the blue vector and the vector that represents the resultant force on the object?

**Q5: **

The resultant force acting on an object is represented by a red vector that is drawn to the scale of the ruler in the diagram with a blue vector representing the horizontal component of the force. The vectors are drawn on a square grid. The sides of the squares are 1 cm long. What is the length of the vector representing the vertical component of the resultant force?

**Q6: **

Some vectors are drawn to the scale of the ruler on a square grid. The sides of the squares are 1 cm long. The red vector is the resultant of the blue and green vectors. What is the length of the resultant vector, measured to the nearest centimeter?

**Q7: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The red vector is the resultant of the blue and green vectors. What is the length of the resultant vector measured to the nearest centimeter?

**Q8: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The green vector is the vertical component of the red vector. What is the length of the horizontal component of the red vector?

**Q9: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The blue vector is the horizontal component of the red vector. What is the length of the vertical component of the red vector measured to the nearest centimeter?

**Q10: **

The forces acting on an object are represented by blue and green vectors that are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The red vector is the resultant of the blue and green vectors. What is the length of the resultant vector, measured to the nearest centimeter?

**Q11: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The green vector is the vertical component of the red vector. What is the length of the horizontal component of the red vector?

**Q12: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The blue vector is the horizontal component of the red vector. What is the length of the vertical component of the red vector measured to the nearest centimeter?

**Q13: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The green vector is the vertical component of the red vector. What is the length of the horizontal component of the red vector measured to the nearest centimeter?

**Q14: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The red vector is the resultant of the blue and green vectors. What is the length of the resultant vector measured to the nearest centimeter?

**Q15: **

The forces acting on an object are represented by blue and green vectors that are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The red vector is the resultant of the blue and green vectors. What is the length of the resultant vector measured to the nearest centimeter?

**Q17: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The blue vector is the horizontal component of the red vector. What is the length of the vertical component of the red vector?

**Q18: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The red vector is the resultant of the blue and green vectors. What is the length of the resultant vector measured to the nearest centimeter?

**Q19: **

Some vectors are drawn to the scale of the ruler in the diagram. The squares of the grid have sides 1 cm in length. The blue vector is the horizontal component of the red vector. What is the length of the vertical component of the red vector?

**Q20: **

The resultant force acting on an object is represented by a red vector that is drawn to scale with a vector representing the vertical component of the resultant force. The vectors are drawn on a square grid. The sides of the squares are 1 cm long, and a distance of one centimeter on the grid represents two newtons of force. What is the size of the horizontal component of the resultant force?

**Q21: **

Some vectors are drawn to the scale of the ruler on a square grid. The sides of the squares are 1 cm long. The red vector is the resultant of the blue and green vectors. What is the length of the resultant vector, measured to the nearest centimeter?

**Q22: **

Two forces acting on an object are represented by black vectors and that are drawn to scale on a square grid. Which vector represents the resultant force on the object?

- AThe red vector
- BThe blue vector
- CThe green vector
- DThe orange vector

**Q23: **

Some vectors are drawn to scale on a square grid. The green vector is the vertical component of the red vector. The blue vector is the horizontal component of the red vector. What is the angle between the red vector and its vertical component?

**Q24: **

Some vectors that represent forces are drawn to scale on a square grid. The sides of the squares are 1 cm long. A distance of 1 cm on the grid represents one newton of force.

What is the difference between the magnitude of the larger horizontal force and the magnitude of the smaller horizontal force?

What is the difference between the magnitude of the larger vertical force and the magnitude of the smaller horizontal force?

**Q25: **

Some vectors are drawn to scale on a square grid. The sides of the squares are 1 cm long. The red vector is the resultant of the blue and green vectors. What is the length of the resultant vector, measured to the nearest centimeter?