Chapter 6 Motion in 2 Dimensions

1. Chapter 6 Motion in 2 Dimensions

2. 6.1 Projectile Motion 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.

3. 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!!

4. By deriving new formulas, We get the following… Vertical motion of a projectile Δy = - ½g(Δt)2 Vyf = -gΔt Vyf2 = -2gΔy

5. Horizontal motion of a projectile Δx = vxΔt vx = vxi = constant R = v02 sinθ g

6. But what if an object is launched At an angle… Δx = vi (cos θ)Δt vx = vi (cos θ) = constant Δy = vi (sin θ)Δt – ½g(Δt)2 vxf = vi(sin θ) - gΔt vyf2 = vi2(sin θ)2 – 2gΔy

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

8. PROBLEM... 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 = 0.86m t = 0.84s

11. 6.2 Circular Motion 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

12. The centripetal force is the Necessary net force exerted in The centripetal direction to Cause circular motion. 4π2r T2 ac = 4π2r T2 Fc = m

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

14. PROBLEM... 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

17. 6.3 Relative Velocity A frame of reference is a Coordinate system for specifying The precise location of objects In space.

18. 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.

19. PROBLEM... 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

20. THE END