2. Chapter 6 Motion in Two Directions Projectile Motion Projectile- object shot through the air Trajectory- the path that a projectile follows How can horizontal and vertical displacement be determined? 1.Vertical displacement d y = ½gt 2 + v i t if v i =0 then d y = ½gt 2 2.Horizontal displacement d x = v x t

3. Example A stone is thrown horizontally at 15m/s. It is thrown from the top of a cliff 44 m high. a.How long does it take the stone to reach the bottom of the cliff? b.How far from the base of the cliff does the stone strike the ground?

4. Example A projectile is launched horizontally from the top of a building with a velocity of 12.7m/s. At what height is the projectile launched if the projectile lands 15.0 m from the side of the building?

5. Projectiles Launched at an Angle A golf ball is hit and leaves the tee with a velocity of 25.0 m/s at 35.0° with respect to the horizontal. What is the horizontal displacement of the ball? V= 25.0 m/s  = 35.0° d x = ? t=?

6. Example A projectile is fired with a velocity of 19.6 m/s at an angle of 60.0° with the horizontal. a.Calculate the vertical and horizontal velocity of the projectile. b.Calculate the time the projectile is in the air. c.Determine the horizontal displacement that the projectile travels. d.Determine the maximum height the projectile reaches.

7. Circular Motion Centripetal acceleration - center-seeking acceleration of an object moving in a circle. How is it determined? A c = v 2 /r or A c = 4  2 r/T 2

8. Centripetal Force Net force directed toward the center of a circle How is it determined? F net = ma c Example: A 13g rubber stopper is attached to a 0.93 m string. The stopper is swung in a horizontal circle, making one revolution in 1.18s. Find the tension force exerted by the string on the stopper.

9. Relative Velocity Motion is relative to an observer Example: A motor boat traveling 6.0 m/s, East encounters a current traveling 3.8 m/s, South. a.What is the resultant velocity? b.If the width of the river is 120 m wide, then how much time does it take the boat to travel shore to shore? c.What distance downstream does the boat reach the opposite shore?