1. TWO DIMENSIONAL AND VARIED MOTION Projectile Motion The Pendulum

2. Projectile Motion A projectile is an object that is thrown into the air. A projectile moves forward due to its inertia. It accelerates downward due to gravity. The path a projectile makes while in the air is a curve called a trajectory.

3. Horizontal Motion Roll a ball along a horizontal surface, and its velocity is constant because no component of gravity acts horizontally. There is no acceleration.

4. Vertical Motion Drop the ball, and it accelerates downward and covers greater vertical distances each second. It accelerates at 9.8 m/s 2.

5. Projectile Motion (see example) (see example) The horizontal component of motion for a projectile is completely independent of the vertical component of motion. The combination of both motions produce the curved path.

6. Velocity of a Projectile at Various Points

7. Projectile Fired at a Steeper Angle

8. Paths of Projectiles Launched at Different Angles -No Air Resistance HEIGHT RANGE 75  60  45  30  15 

9. With No Air Resistance…. 1. The time for a projectile to reach its maximum height equals the time to fall from that height to the ground. 2. The projectile is traveling at the same speed when it returns to the ground as it had when it was released. 3. The vertical velocity of a projectile will be zero at the top of its arc.

10. Satellite A projectile that is moving fast enough that its arc matches the curvature of the earth. Return to Home Page

11. The Pendulum An object that is suspended so that it can swing back and forth about an axis is called a pendulum. The swing of a pendulum is an example of simple harmonic motion, which means it repeats itself over and over.

12. The Pendulum The time of a back-and-forth swing of a pendulum is called the period of a pendulum. It is measured in seconds. The period of a pendulum only depends on the length of the pendulum and the acceleration of gravity. (see example) (see example)

13. Calculating the period of a pendulum Use the equation: Where T= period of pendulum l = length of pendulum g = gravity

14. Calculating the period of a pendulum An astronaut sets up a pendulum on the moon, where gravity is 1.6 m/s 2. If the pendulum is 1 meter long, what will the period of the pendulum be? Return to Home Page