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Projectile Motion

Projectile Motion. Basic Rules 2-D motion – X and Y equations Example 1 – ball dropped from cliff Example 2 – ball thrown horz. from cliff Example 3-4 Symmetric Football Asymmetric Football. Projectile Motion.

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Projectile Motion

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  1. Projectile Motion • Basic Rules • 2-D motion – X and Y equations • Example 1 – ball dropped from cliff • Example 2 – ball thrown horz. from cliff • Example 3-4 • Symmetric Football • Asymmetric Football

  2. Projectile Motion • Break position, velocity, and acceleration into x and y components, solve as separate x and y problems • 2 Independent constant-accelerations problem! • ay = - 9.8 m/s2, ax = 0 m/s2 • ax = -9.8 m/s2proven method of losing 10 pts! • Question: How often does book accelerate toward wall? • vx= v cosӨ , vy= v sinӨ • x and y ONLY connect during obvious event (hitting ground, etc) • Reassemble x and y as last step if requested!

  3. Projectile Motion • X and Y independent!

  4. X and Y equations • Y equations • y = ½ ayt2 + voyt + yo • vy = ayt + voy • vy2 = voy2 + 2 ayy • X equations • x = voxt + xo • vx = vox • Note: x equations are just y equations with ax = 0 !

  5. Starting Examples 1 • Ball falling from 50 m cliff • Time to hit ground • Velocity • Thrown from 50 m cliff at vox = 10 m/s • Time to hit ground (compare fig 3-19) • Velocity in y • Velocity in x • Range in x • Total velocity (vector addition)

  6. Example 2 – Stunt Driver • Example 3-4 • Ball thrown from 50 m cliff, travels 90 m • Time in air determined by y • Range in x determined by vox and time in air • Uniquely determines vox

  7. Example 3 – Syringe Fountain • X and Y Equations • y = ½ ayt2 + voyt (constant acceleration • x = voxt (constant velocity) • Combine and eliminate t • y = ½ (ay/vox2)x2 + (voy/vox)x • Equation of parabola • Public Fountains • Syringe, Bank fountains

  8. Example 4 - Football • Field Goal

  9. Example 4 - Symmetric Football • Football kicked at 20 m/s and θ = 37 • V0x = 20 cosθ, V0y = 20 sin θ • ax = 0 m/s2, ay = -9.8 m/s2 • Time to maximum height • Maximum height • Velocity at maximum height • Range to maximum height • Time to hit ground • Distance at hit ground • Velocity at hit ground

  10. Example 5 - Asymmetric Football • Football kicked at 20 m/s @ 37° - 1 m high • Time to hit ground • Distance to hit ground • Eliminate non-physical time

  11. Example 6 - Asymmetric Football • Will it clear goalposts 3 m high, 30 m from kick? • Strategy • Find time to go 30 m in x direction. • Find how high it is, at that time, in the y direction. • If height greater than 3 m – Field Goal!

  12. Range Equation • X and Y equations • y = ½ gt2 + voyt + yox = voxt + xo • Find time when y = 0 • 0 = ½ gt2 + voyt • t = 0, t = 2voy / g • Then find x • x = voxt = 2voxvoy / g • x = 2vo2sinΘ cosΘ / g • x = vo2sin2Θ / g • Θ = 0 (min), Θ = 90 (min), Θ =45 (max) • Trade-off between x and y motion • Only works for symmetric

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