Mathematical models

D = 1/2at² + v_ot               (equation 1)

a_c = v_T² / r            (equation 3)

Key Principles

1. Assumptions: flat Earth with no atmosphere
2. The vertical acceleration always is the acceleration due to gravity in the downward direction.
3. The horizontal acceleration always is zero.
4. The vertical velocity is variable
5. The horizontal velocity is constant
6. Horizontal and vertical dimensions are independent but are tied together by time.
7. Speeds are symmetrical

1. Centripetal force and acceleration always point toward the center of rotation.
2. Centripetal force and acceleration form a 90 degree angle with the tangential velocity.
3. Centripetal force is the sum of all vector components in the radial direction pointed at the center of rotation.

Problem Solving Tips: Projectile Motion

The key to all projectile motion problems is to treat them as two separate kinematics problems, one in the x-dimension and one in the y-dimension. Write equations until the number of equations matches the number of unknowns, then solve them simultaneously.

1. Note that all projectile motion problems can be solved with  only the equations 1 & 2  shown above in "Mathematical Models".
2. Decide where to locate the origin.
3. Divide your paper into 2 sections. Label one x-dimension and the other y-dimension and keep the appropriate equations in each dimension.
4. When using the equations 1 & 2, use x subscripts for the x-dimension an y subscripts for the y-dimension.
5. Convert starting velocity vectors into x and y components.
6. Write the equations and solve them simultaneously.

Example Problems

Vocabulary