Projectile Motion

1. Projectile Motion

2. Projectile Motion and the Velocity Vector • Any object that is moving through the air affected only by gravity is called a projectile. • The path a projectile follows is called its trajectory.

3. Projectile Motion and the Velocity Vector • The trajectory of a thrown basketball follows a special type of arch-shaped curve called a parabola. • The distance a projectile travels horizontally is called its range.

5. Projectile Motion and the Velocity Vector • The velocity vector(v) is a way to precisely describe the speed and direction of motion. • There are two ways to represent velocity. • Both tell how fast and in what direction the ball travels. • Calculate the magnitude of the velocity (the speed), using the Pythagorean theorem.

6. Vy y x Projectile Motion • When we drop a ball from a height we know that its speed increases as it falls. • The increase in speed is due to the acceleration gravity, g = 9.8 m/s2. Vx

7. Horizontal Speed • The ball’s horizontal velocity remains constantwhile it falls because gravity does not exert any horizontal force. • Since there is no force, the horizontal acceleration is zero (ax = 0). • The ball will keep moving to the right at 5 m/s.

8. Horizontal Speed • The horizontal distance a projectile moves can be calculated according to the formula:

9. Vertical Speed • The vertical speed (vy) of the ball will increase by 9.8 m/sec after each second. • After one second has passed, vyof the ball will be 9.8 m/sec. • After the 2nd second has passed, vywill be 19.6 m/sec and so on.

11. Calculate using projectile motion • A stunt driver steers a car off a cliff at a speed of 20 meters per second. • He lands in the lake below two seconds later. • Find the height of the cliff and the horizontal distance the car travels.

12. Projectiles Launched at an Angle • A soccer ball kicked off the ground is also a projectile, but it starts with an initial velocity that has both vertical and horizontal components. *The launch angle determines how the initial velocity divides between vertical (y) and horizontal (x) directions.

13. Steep Angle • A ball launched at a steep angle will have a large vertical velocity component and a small horizontal velocity.

14. Calculate velocity • A soccer ball is kicked at a speed of 10 m/s and an angle of 30 degrees. • Find the horizontal and vertical components of the ball’s initial velocity.

15. Shallow Angle • A ball launched at a low angle will have a large horizontal velocity component and a small vertical one.

16. Projectiles Launched at an Angle The initial velocity components of an object launched at a velocity vo and angle θ are found by breaking the velocity into x and y components.

17. Range of a Projectile • The range, or horizontal distance, traveled by a projectile depends on the launch speed and the launch angle.

18. Range of a Projectile • The range of a projectile is calculated from the horizontal velocity and the time of flight.

19. Range of a Projectile • A projectile travels farthest when launched at 45 degrees.

20. Range of a Projectile • The vertical velocity is responsible for giving the projectile its "hang" time.

21. Want to know your "Hang Time“? • Run toward a doorway and jump as high as you can, touching the wall or door frame. • Have someone watch to see exactly how high you reach. • Measure this distance with a meter stick. • The vertical distance formula can be rearranged to solve for time:

22. Want to know your "Hang Time“? • Run toward a doorway and jump as high as you can, touching the wall or door frame. • Have someone watch to see exactly how high you reach. • Measure this distance with a meter stick. • The vertical distance formula can be rearranged to solve for time:

23. Projectile Motion and the Velocity Vector Key Question: Can you predict the landing spot of a projectile?