3. Projectile Motion is the motion Of objects moving In two Dimensions under the influence Of gravity. Projectiles follow parabolic paths This path is called the trajectory.

4. Projectile motion is free fall With an initial horizontal velocity. If a ball is dropped, and another Ball is launched horizontally, Neglecting air resistance, They will hit the ground at the Same time!!

5. By deriving new formulas, We get the following… Vertical motion of a projectile Δy = - ½g(Δt) 2 V yf = -gΔt V yf 2 = -2gΔy

6. Horizontal motion of a projectile Δx = v x Δt v x = v xi = constant R = v 0 2 sinθ g

7. But what if an object is launched At an angle… Δx = v i (cos θ)Δt v x = v i (cos θ) = constant Δy = v i (sin θ)Δt – ½g(Δt) 2 v xf = v i (sin θ) - gΔt v yf 2 = v i 2 (sin θ) 2 – 2gΔy

8. Certain angles will travel Distances that are equal to Other angles. 75° = 15° 60° = 30° 45° travels the farthest

9. A ball is launched with an initial Velocity of 4.5 m/s at an angle Of 66° above the horizontal. What Was the maximum height of The ball? How long did it take For the ball to hit the ground? y = 0.86mt = 0.84s

12. Uniform Circular Motion is Motion at constant speed around A circle with a fixed radius. Centripetal Acceleration is the Center directed acceleration of An object in uniform circular motion

13. The centripetal force is the Necessary net force exerted in The centripetal direction to Cause circular motion. a c = 4π2rT24π2rT2 F c = m 4π2rT24π2rT2

14. v v v a r r T = the period, The time needed To one complete revolution

15. 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. 0.34 N

18. A frame of reference is a Coordinate system for specifying The precise location of objects In space.

19. Velocity measurements differ In different frames of reference. For example, if you bounce a ball In an elevator, the ball will fall at g relative to the ground, but Its acceleration will be faster To the elevator when going up.

20. A Boat traveling east at a speed Of 4 m/s. Peter rolls a marble With a velocity of 0.75 m/s north, Straight across the deck. What Is the velocity of the marble Relative to the water? 4.1 m/s at 11° north of east