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2-D Examples

2-D Examples. Questions on Homework Review – Football kick (symmetric/asymmetric) Review – Football field goal (asymmetric) Review – Range equation (symmetric) Problem 26 – Plane dropping supplies Problem 20 – Romeo and Juliet Problem 31 – Projectile from cliff

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2-D Examples

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  1. 2-D Examples • Questions on Homework • Review – Football kick (symmetric/asymmetric) • Review – Football field goal (asymmetric) • Review – Range equation (symmetric) • Problem 26 – Plane dropping supplies • Problem 20 – Romeo and Juliet • Problem 31 – Projectile from cliff • Example – High fly ball (simultaneous equations).

  2. Questions on Homework • ??

  3. Example 4 – Football Kick (symmetric) • 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

  4. Example 5 - Football Kick (asymmetric) • Football kicked at 20 m/s @ 37° - 1 m high • Time to hit ground • Distance to hit ground • Eliminate non-physical time

  5. Example 6 – Field Goal (asymmetric) • 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!

  6. Range Equation (symmetric) • 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!!

  7. Problem 27 – Plane dropping supplies • Y equation determines time in air! • Voy = 0 (horizontal flight) • How far will it travel in x given vo. • Must drop that far in advance.

  8. Problem 20 - Romeo and Juliet

  9. Problem 20 - Romeo and Juliet • What do you know? • vy= 0, y = 4.5 m, a = - 9.8 m/s2 • What tools do you have? • y = ½ at2 + voyt + yo • x = voxt + xo • vy2= voy2 + 2ay • What can you find? • Find voy =9.39 m/s2 • Then find t = 0.958 s (Xwordpuzzle!) • How can you use to find answer? • Given x = 5m, ax = 0 • Know t from above. • vox= vx = x/t = 5.2 m/s.

  10. Problem 31 -Projectile from Cliff

  11. Example - Simultaneous Equations • Sequential problems • Does the football clear the goal, 3 m high and 30 m from the kick? • Does the high fly clear the fence 10 m high and 95 m from home plate? • Simultaneous problems • When Babe Ruth hit a homer over the 12 m high right-field fence 95 m from home plate, roughly what was the minimum speed of the ball when it left the bat? Assume the ball was hit 1.0 m above the ground and its path initially made a 40° angle with the ground. • 12 m = ½ (-9.8 m/s2) t2 + vo sin(40) t + 1m • 95 m = vocos(40) t • t = 95 m / vocos(40) • t = 3.74 s • vo == 33.16 m/s

  12. Problem 26 – Hunter aims at target • Fired horizontal – How much will miss? • Fired at angle – What angle? • X equation to range • Y equation to zero • Range equation (symmetric)

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