Vectors

• Idea: What are vectors and scalars?
• Representing vectors: Graphically (arrows in the plane), by magnitude and direction, and by components.
• Conversion: Between magnitude/direction and components, using

V_x = V cos , V_y = V sin ,   and   V = (V_x² + V_x²)^1/2 , = arctan (V_y/V_x).

• Adding vectors: Graphically (tail-to-tip or parallelogram method); Analytically (by adding components).
• Other operations: Subtracting vectors, and multiplying by a scalar, both graphically and analytically.

2-Dimensional Motion

• Main idea: If the acceleration in each of the two dimensions does not depend on the motion in the other dimension, the two motions can be analyzed using separate equations. However, the two motions take place simultaneously, so the time t is the same, and information from both may be put together into vectors.

Projectile Motion and Problems

• Concept: A motion in two dimensions (horizontal and vertical) that takes place in air or a vacuum, with no forces other than gravity acting (for example, air resistance if present is neglected). The horizontal motion has constant velocity, the vertical one constant acceleration of magnitude g.
• Problems on two objects that meet: Write the equations for the motion of both objects; The two will meet if their positions are the same for some common value of t. To solve the problem, just use equations for both objects, where their x, y and t are the same.