1 / 16

7-2 Projectile Motion

7-2 Projectile Motion. Independence of Motion in 2-D. Projectile is an object that has been given an intial thrust (ignore air resistance) Football, Bullet, Baseball Moves through the air under the force of gravity Path is called Trajectory

eve
Download Presentation

7-2 Projectile Motion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 7-2 Projectile Motion

  2. Independence of Motion in 2-D • Projectile is an object that has been given an intial thrust (ignore air resistance) • Football, Bullet, Baseball • Moves through the air under the force of gravity • Path is called Trajectory • If you know the force of the thrust, you can determine trajectory

  3. Independence of Motion in 2-D If you hit a golf ball, throw a football, only force acting on the projectile is gravity (long range) Gravity acts same in vertical direction Horizontal force has no effect on vertical component

  4. Combination of vertical drop and horizontal moment give object a parabola trajectory

  5. Strategy • Separate into vertical and horizontal motion problem • Vertical motion is treated like a straight up or down movement (g) • Horizontal motion treated like a constant velocity problem • No thrust and air drag neglected • No horizontal forces acting (a = 0) • Motions are connected by time variable • Solve for time in one of the dimensions and will give you other

  6. Equations • Y-direction: vy = -gt • y = y0 – (1/2)gt2 • t = √ -2(y – y0) g • X-Direction • x = x0 + vx0t

  7. Stone is thrown horizontally at 15 m/s from top a cliff 44 meters high • A) How far from the base of the cliff does the stone hit the ground? • Known • X0 = 0 vx0 = 15 m/s y0 = 0 vy0 = 0 a = -g • Unknown • X when y = -44 m • V at that time a Fg = Fnet

  8. How far from the base of the cliff does the stone hit the ground? • Y-direction • y = y0 – (1/2)gt2 • t = √-2(y-y0) so: = √ -2(y) / g g • √ -2(-44 ) / -9.8 m/s2 • = 3.0 sec

  9. How far from the base of the cliff does the stone hit the ground? • X direction • x = x0 + vx0t • x = (15 m/s)(3.0 m/s) • = 45 meters from the base

  10. How fast is it moving the instant before it hits the ground? Vy = -gtvx = -(9.80 m/s2)(3.0 s) = -29 m/s vy v v =√ vx2 + vy2 = √(15 m/s)2 + (-29 m/s)2 = 33 m/s

  11. Projectiles Launched at an Angle • Initial velocity has an initial horizontal and vertical component • Rises with slowing speed and falls with gaining speed • Max Height • height of projectile when vertical velocity is zero and only has horizontal component • y = yi + Vyit – (1/2)gt2 • Range (R) • Horizontal distance the projectile travels

  12. Problem • A ball is launched with an initial velocity of 4.47 m/s at an angle of 66o above the horizontal. • A) What is the max height the object attained? • B) How long did it take the ball to return to the launching height? • C) What was the range? • Known • xi = 0 yi= 0 vi = 4.47 m/s θ = 66o a = -g • Unknown • y when Vy = 0 t = ?? x when y = 0

  13. Equations Needed • Y direction: • Vyi = vi sinθ (4.47)sin 66o • Vyi = 4.08 m/s • *** Vy = Vyi – gt • *** y = yi + Vyit – (1/2)gt2 • x direction • Vxi = vicosθ • Vx = Vxi • x = xi + vxit

  14. What is the max height the object attained? Vy = 0, t = vyi / g t = (4.08 m/s) / (9.80 m/s2) t = 0.420 s y max = vyit – (1/2)gt2 = (4.08 m/s)(0.420) – (1/2)(9.80)(0.420)2 y max = 0.850 m

  15. How long did it take the ball to return to the launching height? y = 0 y = yi + Vyit – (1/2)gt2 0 = 0 + Vyit – (1/2)gt2 t = 2vyi / g = 2(4.08 m/s) / (9.80) t = 0.83

  16. What was the range? x = R R = Vxit = (4.47 m/s)(cos 66o)(0.83 s) R = 1.5 m

More Related