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Projectile Motion 2.ppt
- 1.
- 2. Objects in projectilemotion follow a parabolic path called a trajectory.
- 3. If released atthe same instant, a bullet shot from a gun will hit the ground at the same time as a bullet dropped from the same height.
- 4. The horizontal andvertical motions of a projectile are independent, meaning they do not affect each other. Horizontal motion Vertical motion
- 5. The 2-D motionof a projectile can be separated into two 1-D motions: horizontal and vertical.
- 6.
- 7. The horizontal motionof a projectile is always constant, if we neglect air resistance.
- 8. For projectiles shotat 0°, all of the initial velocity is in the x direction. Thus, Vyi = 0 m/s.
- 9. For projectiles shotat 0°, vertical displacement and velocity will always be negative.
- 10. To hit thetarget, when should you release the package?
- 11. Rules for ProjectileMotion • Treat horizontal and vertical as two separate sides of the problems • TIME is the key, and the only variable that can be used for both horizontal and vertical • Horizontal Motion is always constant • vx is constant • ax = 0 m/s2 • Objects follow a parabolic shape
- 12. Horizontal Projectile Motion •All of the initial velocity is in the x direction, Vyi = 0 m/s • Vertical displacement and velocity will always be negative
- 13.
- 14. APM: Angled ProjectileMotion
- 15. For projectiles shotat an angle, initial velocity is both vertical and horizontal.
- 16. Horizontal velocity andinitial vertical velocity can be found using trig functions. Vx = Vi Cos θ Vyi Vx Vi θ Vyi = Vi Sin θ
- 17. At the endof the problem, you can recombine horizontal and vertical velocity to get the total 2-D velocity. Vx Vyf Vf Vx Vyf Vf Vf 2 = Vx 2 + Vyf 2 θ θ = tan-1(Vyf / Vx)
- 18. For APM, vyat any height is the same while going up and coming down except for direction.
- 20. Velocities of projectilemotion Note: Vy = 0 at the highest point.
- 21. With air resistance,the actual path is shorter.
- 22. Angled Projectile Motion •Initial velocity is both vertical and horizontal • Use trig functions to find vyi and vx • Vx = Vi Cos θ • Vyi = Vi Sin θ • Remember clues • vy at the top is 0 m/s • vy at any height is the same while going up and coming down except for direction
- 23. Example Problem Happy Gilmorehits his shot at 55.0 m/s with an angle of 50.0° to the ground. How far did the ball travel before it lands? •vi = 55.0 m/s •θ = 50.0° •ay = -9.81 m/s2 •∆x = ?
- 24. vi = 55.0m/s ay = -9.81 m/s2 ∆x = ? θ = 50.0° • Find vx and vyi vx = vi Cos θ = 55.0 m/s Cos (50.0°) = 35.4 m/s vyi = vi Sin θ = 55.0 m/s Sin (50.0°) = 42.1 m/s
- 25. vi = 55.0m/s ay = -9.81 m/s2 ∆x = ? θ = 50.0° vyi = 42.1 m/s vx = 35.4 m/s • What do we need to find ∆x? • Time! Find time from the vertical side • ∆y = vyi ∆t + ½ ay ∆t2 0 m = (42.1 m/s) ∆t + ½ (-9.81 m/s2) ∆t2 - (42.1 m/s) ∆t = ½ (-9.81 m/s2) ∆t2 (42.1 m/s) = ½ (9.81 m/s2) ∆t ∆t = 8.58 s
- 26. vi = 55.0m/s ay = -9.81 m/s2 ∆x = ? θ = 50.0° vyi = 42.1 m/s vx = 35.4 m/s ∆t = 8.58 s • Now we can find ∆x • ∆x = vx ∆t = (35.4 m/s)(8.58 s) = 304 m
- 27. Where Should WeAim the Cannon? At or Above the monkey?
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- 29.
- 30. Explanation of monkeyexperiment
- 31. Ranges of projectilesversus angle.
- 32.
- 33. If speed isgreat enough…
- 34. That’s how thespace shuttle and satellites orbit the earth.