HW #6 - Resolving Vectors into Components

Front

What is a vector quantity?

Back

A vector quantity is defined as a quantity that has both magnitude and direction.

Front

How do you find the vertical component of a vector given its magnitude and angle?

Back

The vertical component (Vy) can be found using the formula: Vy = V * sin(θ), where V is the magnitude and θ is the angle with the horizontal.

Front

How do you find the horizontal component of a vector given its magnitude and angle?

Back

The horizontal component (Vx) can be found using the formula: Vx = V * cos(θ), where V is the magnitude and θ is the angle with the horizontal.

Front

What is the formula to calculate the magnitude of a vector given its components?

Back

Front

What is the significance of the angle in vector resolution?

Back

The angle determines how much of the vector's magnitude is allocated to the horizontal and vertical components.

Front

If a vector has a magnitude of 10 units and is at an angle of 45 degrees, what are its components?

Back

The components are: Vx = 10 * cos(45°) = 7.07 units and Vy = 10 * sin(45°) = 7.07 units.

Front

What is the relationship between degrees and radians in vector calculations?

Back

Angles can be expressed in degrees or radians; to convert degrees to radians, use the formula: radians = degrees * (π/180).

Front

What is the horizontal component of a force vector?

Back

The horizontal component of a force vector can be calculated using: F_x = F * cos(θ), where F is the force and θ is the angle above the horizontal.

Front

What is the vertical component of a force vector?

Back

The vertical component of a force vector can be calculated using: F_y = F * sin(θ), where F is the force and θ is the angle above the horizontal.

Front

How do you resolve a vector into its components?

Back

To resolve a vector, use trigonometric functions (sine and cosine) based on the angle of the vector with respect to the horizontal.