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Projectile Motion

Projectile Motion. Projectile Velocities. Sammy ACT:.

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Projectile Motion

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  1. Projectile Motion

  2. Projectile Velocities

  3. Sammy ACT: • Sammy Sosa clobbers a fastball toward center-field. The ball is hit 1 m (yo) above the plate, and its initial velocity is 36.5 m/s(vo) at an angle of 30o () above horizontal. The center-field wall is 113 m(x) from the plate and is 3 m(h) high. • What time does the ball reach the fence? • Does Sammy get a home run? • In other words, will the ball clear the fence? vo  h y0 x

  4. Sammy ACT: • Choose y axis up. • Choose x axis along the ground in the direction of the hit. • Choose the origin (0,0) to be at the plate. • Say that the ball is hit at t = 0, x = x0 = 0 y vo  y y0 x x

  5. Sammy ACT Equations of motion are: Horizontal Vertical vx = constant vy = vy0 - gt x = vxt y = y0 + vy0 t - 1/ 2 gt2 Remember that the horizontal and vertical motions are Independent of one another, but they share the time. Variables: v0 = 36.5 m/s t = ???  = 30o is y > h = 3 m??? y0 = 1 m x = 113 m

  6. Sammy... • Use geometry and trigonometry to figure out vx and vy0 : g Find vx = v cos . and vy = v sin . y 36.5 m/s v0 vy0  300 vx = 36.5 cos(30o) m/s = 31.6 m/s y0 vx vy0 = 36.5 sin(30o) m/s = 18.25 m/s x

  7. Sammy ACT • We can use the horizontal motion equation to determine the time to reach the wall: • x = vx t • t = x / vx • t = (113 m) / (31.6 m/s) = 3.58 s • We have an equation that tells us y(t) = y0 + vy0 t + a t2/ 2 y(t) = (1.0 m) + (18.25 m/s)(3.58 s) - (0.5)(9.8 m/s2)(3.58 s)2 = (1.0 + 65.3 - 62.8) m = 3.5m • Since the wall is 3 m high, Sammy gets the homer!!

  8. Projectile Range Equations of motion are: Horizontal Vertical vx = constant vy = vy0 - gt x = vxt y = y0 + vy0 t - 1/ 2 gt2 • Equations for x and y can be combined (click here to see the derivation) to yield the following equation:

  9. Range of Projectile

  10. Golf Range ACT • A golf ball is chipped at an angle of 46o and with a speed of 5.4 m/s. How far does it travel to the nearest tenth of a meter?

  11. Projectile Launched at Angle

  12. Feeding the Monkey(Banana Gun) • Where does the zookeeper aim if he wants to hit the monkey? • ( He knows the monkey willlet go as soon as he shoots ! )

  13. Feeding the Monkey... r = r0 • If there were no gravity, simply aim at the monkey r =v0t

  14. Banana hits monkey! Feeding the Monkey... r= r0 - 1/2 g t2 • With gravity, still aim at the monkey! r= v0t - 1/2 g t2

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