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Chapter 4 Motion in Two Dimensions EXAMPLES

Chapter 4 Motion in Two Dimensions EXAMPLES. Example 4.1 Driving off a cliff. y i = 0 at top, y is positive upward. Also v yi = 0 How fast must the motorcycle leave the cliff to land at x = 90 m, y = – 50 m Unknown: v xi = ? Formulas: v y =  gt

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Chapter 4 Motion in Two Dimensions EXAMPLES

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  1. Chapter 4 Motion in Two Dimensions EXAMPLES

  2. Example 4.1 Driving off a cliff. • yi = 0 at top, y is positive upward. Also vyi = 0 • How fast must the motorcycle leave the cliff to land at x = 90 m, y = – 50 m • Unknown:vxi = ? • Formulas: vy = gt x = vxit y = ½gt2 • Time to Bottom: • vxi = x/t = 90.0m/3.19s  vxi = 28.2 m/s

  3. Example 4.2 Kicked football • Given: θi= 37º, vi= 20 m/s vxi = vicosθi = 16 m/s & vyi= visinθi = 12 m/s • Find a. Max height (h) ? b. Time when hits ground? c. Total distance traveled in the x direction (R) ? d. Velocity at top? e. Acceleration at top? vi vyi vxi

  4. Example 4.2 cont.

  5. A child sits in a wagon, moving to the right (x-direction) at constantvelocityvox. She throws an apple straight up (from her viewpoint) with initial velocity voywhile she continues to travel forward atvoxNeglect air resistance. Will the apple land behind the wagon, in front of the wagon, or in the wagon? Example 4.3 Where Does The Apple Land?

  6. The apple will stay above the girl the entire trip and will land in the wagon. The reason is: To a person in the ground reference frame (b) the apple will be exactly a projectile in motion (neglecting air resistance). To the girl it is an object in free fall. And the Vertical motion of a projectile and free fall are the same. Example 4.3 Cont.

  7. “Shooting the Monkey”!! A boy on a small hill aims his water-balloon slingshot horizontally, straight at a second boy hanging from a tree branch a distance daway. At the instant the water balloon is released, the second boy lets go an fall from the tree, hopping to avoid being hit. Show that he made the wrong move (He hadn’t studied Physics yet!!) Example 4.4 Wrong Strategy (Similar to Example 4.3 Text Book)

  8. “Shooting the Monkey”!! Both the water balloon and the boy in the tree start falling at the same time, and in a time t they each fall the same vertical distance y = ½gt2 In the same time it takes the water balloon to travel the horizontal distance d, the balloon will have the same y position as the falling boy. Splash!!! If the boy had stayed in the tree, he would have avoided the humiliation Example 4.4 Cont.

  9. Example 4.5 That’s Quite an Arm • Non-Symmetric Projectile Motion • Example 4.4 (text book), page 84 • Follow the general rules for projectile motion • Break the y-direction into parts • up and down or • symmetrical back to initial height and then the rest of the height • May be non-symmetric in other ways

  10. Example 4.5 Cont. • Given: θi= 30º, vi= 20 m/s  • (A) vxi= vicosθi = 17.3 m/s and vyi= visinθi = 10.0 m/s At t = 0 : xi = 0 yi = 0 • Find: t = ? (time at which the stone hits the ground)withyf = – 45.0m • Using: yf =vyit – ½gt2  – 45.0m = (10.0m/s)t – (4.90m/s2)t2 • Solving for t using General Quadratic Formula: t = 4.22 s • (B) vxi= vxf = 17.3 m/s and vyf = vyi – gt  vyf = 10.0m/s – (9.80m/s2)(4.22s) vyf = ̶ 31.4m/s

  11. Example 4.6 The End of the Ski Jump • Example 4.5 (text book), page 85 • Given the figure of the ski jumper, find the distance d traveled along the incline. 1. Coordinates xand y at the end: 2. From the figure:

  12. Example 4.6 Cont. 3. Equating (1) = (3) and (2) = (4) 4. Dividing (6) by (5): 5. Substitution of (7) in (5) and solving for d: 6. Substitution of d into (3) and (4), gives the coordinates:

  13. Example 4.7 The Centripetal Acceleration of the Earth • Calculate ac of the Earth, assuming it moves in a circular orbit around the Sun. • Note that ac<<g

  14. Material for the Midterm • Material from the book to Study!!! • Objective Questions: 1-4-6 • Conceptual Questions: 5-6-7 • Problems: 2-4-6-10-11-21-27

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