Mr. Rogers AP Physics C Study Guide  --  Projectile Motion, Circular Motion

Unit Plan Practice Test Study Guide

Mathematical models

Projectile Motion (Constant Downward Acceleration)

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

Circular Motion (Constant Magnitude of Tangential Velocity)

ac = vT2 / r            (equation 3)

v = at + vo                         (equation 2) T = (2pr) / vT        (equation 3)

Key Principles

Projectile Motion
  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
Circular Motion
  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

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

Projectile Motion
Bomber Problem
A WWII Bomber from an aircraft carrier flying at an altitude of 3000 m and a horizontal velocity of 100 m/s drops a bomb. Find the horizontal distance the bomb travels before hitting the ground.
Artillery's Range Problem
An  artillery shell is fired at an angle of 30 with respect to the horizon with an initial velocity of 760 m/s. Find the range of the artillery shell.
Anti-Balloon Gun Problem
An observation balloon floats over the Enemy lines and the defenders decide to shoot it down. The defending gunners determine the balloon is 3015 m above the ground at a distance of 5000 m. They fire a cannon at an angle of 40 with respect to the horizon with an initial velocity of 760 m/s.





centripetal acceleration centripetal force tangential velocity
parabolic range trajectory

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