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Understanding Free Fall and Projectile Motion: Key Concepts and Equations

This text explores the concepts of free fall and projectile motion. Free fall occurs when an object is acted on solely by gravity, with an acceleration of approximately 10 m/s². It discusses the equations governing the motion: the distance traveled (d = ½ gt²) and the instantaneous velocity (v = gt). Furthermore, it examines projectile motion, which involves horizontal velocity and vertical acceleration under gravity. Key differences between free fall, horizontal projection, and angled projection are highlighted, including factors affecting time of flight and range.

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Understanding Free Fall and Projectile Motion: Key Concepts and Equations

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  1. Tueday, Mar. 11 Do Now What is free fall?

  2. -Free fall is the motion of an object being acted on only by gravity. -Acceleration due to gravity is approximately 10 m/s2. -An object dropped from rest will accelerate from a velocity of zero to 10 m/s after dropping 1 meter. acceleration due to gravity = g= 10 m/s2 -If an object is thrown upwards, it will decelerate (have negative acceleration or slow down) at a rate of 10 m/s2. -The instantaneous velocity of an object falling from rest after a time interval of t is: v = gt -The distance traveled by an object in free fall is given by: d = ½ gt2 Summary of Chapter 2 – Free Fall

  3. -The distance traveled and velocity of an object being accelerated by any force is given by: d = ½ a t2 v = at

  4. Introduction • Projectile Motion: Motion through the air without a propulsion • Examples:

  5. Motion of Objects Projected Horizontally

  6. y x

  7. y x

  8. y x

  9. y • Motion is accelerated • Acceleration is constant, and downward • a = g = -9.81m/s2 • The horizontal component of velocity is constant • The horizontal and vertical motions are independent of each other, but they have a common time g = -9.81m/s2 x

  10. ANALYSIS OF MOTION ASSUMPTIONS: • x-direction (horizontal): uniform motion • y-direction (vertical): accelerated motion • no air resistance QUESTIONS: • What is the trajectory (path of motion)? • What is the total time of the motion? • What is the horizontal range? • What is the final velocity?

  11. Wednesday, Mar. 12 Do NowWhich object hits the ground first:-an object dropped from rest, or-an object that is moving with a horizontal velocity before being dropped? Explain why.

  12. y v0 g h x 0 Frame of Reference: Equations of motion:

  13. y h v02 > v01 v01 x Trajectory x = v0 t y = h + ½ g t2 Parabola, open down

  14. y h x Total Time, Δt Δt = tf - ti Total time of motion depends only on the initial height, h ti =0 tf =Δt

  15. y h Δx x Horizontal Range, Δx x = v0 t Horizontal range depends on the initial height, h, and the initial velocity, v0

  16. Thursday, Mar. 13 Do NowWhich object hits the ground first:-an object dropped from rest, or-an object that is moving with a horizontal velocity before being dropped? Explain why.

  17. y v0 g h x 0 Frame of Reference: Equations of motion:

  18. y h v02 > v01 v01 x Trajectory x = v0 t y = h + ½ g t2 Parabola, open down

  19. y h x Total Time, Δt Δt = tf - ti Total time of motion depends only on the initial height, h ti =0 tf =Δt

  20. y h Δx x Horizontal Range, Δx x = v0 t Horizontal range depends on the initial height, h, and the initial velocity, v0

  21. Wed. March 19 Do Now:In the Bull’s Eye lab, what is the formula you used to calculate:speed of your marble:the time is takes for the marble to fall to the ground:

  22. So far we have looked at motion of objects in free fall and motion as an object is projected horizontally. Now we will look at objects projected at an angle.

  23. Examples:Free FallObject projected horizontally

  24. Examples of Projectiles at an Angle

  25. y a = g = - 9.81m/s2 • Motion is accelerated • Acceleration is constant, & downward • a = g = -9.81m/s2 • The horizontal (x) component of velocity is constant. The horizontal & vertical motions are independent of each other, but they have a common time. x

  26. ANALYSIS OF MOTION: ASSUMPTIONS • x-direction (horizontal): constant velocity • y-direction (vertical): accelerated motion • no air resistance QUESTIONS • What is the path of motion? • What is the total time of the motion? • What is the horizontal range? • What is the maximum height? • What is the final velocity?

  27. Path Of Motion – parabola, open down y Assumes no air resistance x 0 Δx Δx is the horizontal range

  28. Trajectory and horizontal range • CONCLUSIONS: • Horizontal range is greatest for the throw angle of 450 • Horizontal range is the same for 30o & 60o launch angles. gree vi = 25 m/s

  29. Velocity • Final speed = initial speed (conservation of energy) • Impact angle = - launch angle (symmetry of parabola)

  30. PROJECTILE MOTION - SUMMARY • Projectile motion is motion with a constant horizontal velocity combined with a constant vertical acceleration • The projectile moves along a parabola

  31. Class Work/Homework • P. 40-42 #7-10, 12-14, 34, 42-44, 46

  32. Thurs. March 20 Do Now: • Describe the differences between free fall, motion of an object projected horizontally, and motion of an object projected at an angle. • Two objects projected from a cliff at the same time. One object is dropped straight down from the cliff. The other object is pushed off the cliff horizontally with a velocity of 10 m/s. Which one will hit the ground first?

  33. Shooting rubber balls out of fixture demo • Review of projectiles • Quiz

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