1. Projectile Motion

2. 2 components of all projectile motion: Horizontal component (vx) is constant. Vertical component (vy) is affected by gravity.

4. Two types to consider: Two types to consider: Horizontal projection Horizontal projection Ball rolling off of tabletop. Ball rolling off of tabletop. Bullet fired horizontally from rifle. Bullet fired horizontally from rifle. Angled projection Angled projection Cannonball fired at angle. Cannonball fired at angle.

5. Horizontal Projection A ball rolls off a tabletop that is 0.750 m above the floor with an initial speed of 2.00 m/s. A ball rolls off a tabletop that is 0.750 m above the floor with an initial speed of 2.00 m/s.

6. Horizontal Projection A ball rolls off a tabletop that is 0.750 m above the floor with an initial speed of 2.00 m/s. A ball rolls off a tabletop that is 0.750 m above the floor with an initial speed of 2.00 m/s. How long does the ball take to hit the floor? How long does the ball take to hit the floor? Ball has no original vertical velocity. Ball has no original vertical velocity. Downward displacement = -0.750 m. Downward displacement = -0.750 m. Acceleration due to gravity = -9.81 m/s 2 Acceleration due to gravity = -9.81 m/s 2  x = ½at 2  x = ½at 2 (-0.750 m) = ½ (-9.81 m/s 2 ) t 2 (-0.750 m) = ½ (-9.81 m/s 2 ) t 2 (-0.750 m) = (-4.91 m/s 2 ) t 2 (-0.750 m) = (-4.91 m/s 2 ) t 2 t 2 = 0.153 s 2 t 2 = 0.153 s 2 t = 0.391 s t = 0.391 s

7. Horizontal Projection A ball rolls off a tabletop that is 0.750 m above the floor with an initial speed of 2.00 m/s. A ball rolls off a tabletop that is 0.750 m above the floor with an initial speed of 2.00 m/s. How far from the base of the table does the ball land? How far from the base of the table does the ball land? Ball is airborne for 0.391 s. Ball is airborne for 0.391 s. Ball’s horiz. speed is 2.00 m/s. Ball’s horiz. speed is 2.00 m/s. s = d/t s = d/t d = st = (2.00 m/s)(0.391 s) = 0.782 m d = st = (2.00 m/s)(0.391 s) = 0.782 m

8. Horizontal Projection A car rolls off of a cliff (don’t worry, the driver jumped free at the last second!) at 30.0 m/s and hits the ground 3.50 seconds later. A car rolls off of a cliff (don’t worry, the driver jumped free at the last second!) at 30.0 m/s and hits the ground 3.50 seconds later. How tall is the cliff? How tall is the cliff? How far from the cliff’s base did the car land? How far from the cliff’s base did the car land?

9. Horizontal Projection A rifle bullet is fired horizontally from a height of 1.60 m. The rifle bullet lands 487 m away. A rifle bullet is fired horizontally from a height of 1.60 m. The rifle bullet lands 487 m away. How long is the bullet airborne? How long is the bullet airborne? What was the original speed of the bullet? What was the original speed of the bullet?

10. Angled Projection When a projectile is fired at an angle, calculate both the horizontal and vertical components. When a projectile is fired at an angle, calculate both the horizontal and vertical components. Vertical component affected by gravity. Vertical component affected by gravity. Horizontal remains constant. Horizontal remains constant.

11. Angled Projection A cannon fires a shell at 150. m/s at an angle of 30º above the horizon. A cannon fires a shell at 150. m/s at an angle of 30º above the horizon. What is the shell’s horizontal velocity? What is the shell’s horizontal velocity? (150. m/s)(cos30º) = 130. m/s (150. m/s)(cos30º) = 130. m/s What is the shell’s initial vertical velocity? What is the shell’s initial vertical velocity? (150. m/s)(sin30º) = 75.0 m/s (150. m/s)(sin30º) = 75.0 m/s 30º 150. m/s

12. Angled Projection An archer fires an arrow with v o of 45.0 m/s at an angle 40º above the horizontal. An archer fires an arrow with v o of 45.0 m/s at an angle 40º above the horizontal. What is the maximum height attained by the arrow? What is the maximum height attained by the arrow? How long is the arrow in flight? How long is the arrow in flight? How far from the archer does the arrow land? How far from the archer does the arrow land?

13. Angled Projection A catapult lobs a stone at 30.0 m/s at an angle 70º above the horizon. A catapult lobs a stone at 30.0 m/s at an angle 70º above the horizon. What is the maximum height obtained by the stone? What is the maximum height obtained by the stone? How long is the stone in the air? How long is the stone in the air? How far from the catapult does the stone land? How far from the catapult does the stone land?