Exploring Vectors

Olivia is trying to understand the difference between a vector and a scalar in her physics class. She learns that a vector has both magnitude and direction, while a scalar has only magnitude. Can you help her clarify this concept?

• A vector has only magnitude, while a scalar has both magnitude and direction.

• A vector has both magnitude and direction, while a scalar has only magnitude.

• A vector can only be represented in two dimensions, while a scalar can be in any dimension.

• A vector is a single point in space, while a scalar is a line.

Imagine or draw a vector representing a force of 5 N at an angle of 30 degrees. What are its components?

• x-component: 2.5 N, y-component: 4.33 N

• x-component: 3 N, y-component: 4 N

• x-component: 4.33 N, y-component: 2.5 N

• x-component: 5 N, y-component: 0 N

Using masking tape, create a right triangle with sides representing vectors A and B. What is the resultant vector?

• R = A + B

• R = √(A² + B²)

• R = A × B

• R = A - B

Oliver is trying to find the position of a point in a park using polar coordinates. He wants to convert these coordinates to Cartesian coordinates to better understand the layout of the park. How does he convert a vector from polar coordinates to Cartesian coordinates?

• x = r * sin(θ), y = r * cos(θ)

• x = θ * cos(r), y = θ * sin(r)

• x = r + θ, y = r - θ

• x = r * cos(θ), y = r * sin(θ)

If vector A has a magnitude of 10 units and is directed along the positive x-axis, what are its Cartesian components?

• (10, 0)

• (10, 10)

• (5, 5)

• (0, 10)

Explain how to add two vectors graphically using the head-to-tail method.

• You add the vectors by placing them side by side without connecting them.

• The resultant vector is the average of the two vectors' lengths.

• The resultant vector is obtained by drawing from the tail of the first vector to the head of the second vector.

• The resultant vector is drawn from the head of the first vector to the tail of the second vector.

What is the significance of the angle in polar coordinates?

• The angle represents the distance from the origin.

• The angle is irrelevant in polar coordinates.

• The angle determines the size of the point.

• The angle indicates the direction of a point in polar coordinates.

William and Avery are using ping pong balls to demonstrate the concept of vector addition by rolling two balls in different directions. What do you observe?

• The resultant direction and distance of the combined movement of the two balls illustrate vector addition.

• The balls will bounce off each other without any direction change.

• Rolling the balls in the same direction will cancel each other out.

• The combined movement will always go straight regardless of the angles.

How do you find the magnitude of the resultant vector when adding two vectors at right angles?

• R = A + B

• R = A - B

• R = √(A² + B²)

• R = A × B

What are the steps to resolve a vector into its components using trigonometric functions?

• Vx = V + cos(θ), Vy = V + sin(θ)

• Vx = V / cos(θ), Vy = V / sin(θ)

• Vx = V * cos(θ), Vy = V * sin(θ)

• Vx = V * tan(θ), Vy = V * sec(θ)