1. AP PHYSICS Chapter 3 2-D Kinematics

2. 2-D MOTION The overriding principle for 2-Dimensional problems is that the motion can be resolved using vectors in the x & y direction. The motion in each direction is independent of the motion in the other direction. So, analysis of 2-D motion is accomplished by solving two one dimensional problems.

3. PROBLEM SOLVING STRATEGY Select a coordinate system Sketch and label all vectors Find x & y components for vectors Add all x components and all y components to determine the resultant vector’s components.

4. PROBLEM SOLVING STRATEGY Use the Pythagorean theorem to find the magnitude of the resultant vector Use suitable trig function to find the angle the resultant makes with the x axis.

5. PROJECTILE MOTION Free fall acceleration (g) is constant over the motion Air resistance is negligible Rotation of earth does not affect motion.

6. PROJECTILE MOTION For the horizontal motion, acceleration is zero. For the vertical motion, the analysis of the motion is identical to free-fall.

7. PROJECTILE MOTION RANGE For projectile motion, the range (R), is the maximum horizontal distance.

8. PROJECTILE MAXIMUM HEIGHT

9. PROJECTILE MOTION PROBLEM 1. A motorcycle speeds horizontally off a 50.0 m high cliff. How fast must it leave the cliff to land 90.0 m from the base of the cliff?

10. PROJECTILE MOTION PROBLEM 2. A football is kicked at an angle of 37.0° with the horizontal at a velocity of 20.0 m/s. Calculate (a) maximum height, (b) total time in the air, (c) how far away it hits the ground, (d) velocity vector at max. height, & (e) the acceleration vector at max. height.

11. PROJECTILE MOTION PROBLEM 3. A child in a wagon moving at a constant velocity throws an apple vertically upward, where does it land? 4. A boy on a hill aims a water balloon horizontally at another boy at the same height hanging from a tree branch. The boy in the tree lets go and falls at the same instant that the balloon is shot. Was this strategy sound?

12. PROJECTILE MOTION PROBLEM 5. Suppose a football leaves a punter’s foot at a height of 1.00 m above the ground with an angle of 37.0° and a velocity of 20.0 m/s. How far will the football travel before hitting the ground?