Increases the range.

Increases the object's acceleration (Newton's Second Law).

The object remains at rest or continues to move at a constant velocity (Newton's First Law).

Increases the frictional force between the surfaces.

It becomes zero.

A quantity with both magnitude and direction.

The single vector representing the overall effect of multiple vectors.

Projections of a vector onto coordinate axes (e.g., x and y).

The length or size of the vector, representing the quantity's amount.

The horizontal component of a vector, found using $A_x = A \cos \theta$.

The vertical component of a vector, found using $A_y = A \sin \theta$.

Use the Pythagorean theorem: $R = \sqrt{A_x^2 + A_y^2}$.

Use trigonometry: $A_x = A \cos \theta$ and $A_y = A \sin \theta$, where $\theta$ is the angle with respect to the positive x-axis.

1. Resolve A and B into x and y components. 2. Add the x-components: $R_x = A_x + B_x$. 3. Add the y-components: $R_y = A_y + B_y$. 4. Find the magnitude of R: $R = \sqrt{R_x^2 + R_y^2}$. 5. Find the direction of R: $\theta = \tan^{-1}(R_y / R_x)$.

1. Resolve initial velocity into horizontal and vertical components. 2. Analyze horizontal motion (constant velocity). 3. Analyze vertical motion (constant acceleration due to gravity). 4. Use kinematic equations to find unknowns (time, range, max height).

1. Identify the object of interest. 2. Represent the object as a point. 3. Draw and label all forces acting on the object (gravity, normal force, friction, applied forces). 4. Ensure forces are drawn in the correct direction.

1. Draw a free-body diagram. 2. Resolve gravitational force into components parallel and perpendicular to the incline. 3. Calculate the normal force. 4. Calculate the frictional force (if any). 5. Sum the forces along the incline to find the net force.