Chapter 4 Motion in Two Dimensions EXAMPLES

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Chapter 4 Motion in Two DimensionsEXAMPLES
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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

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Example 4.2 Kicked football
vi
vyi
vxi

• Given ?i 37º, vi 20 m/s
• vxi vicos?i 16 m/s vyi visin?i
  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?

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Example 4.2 cont.
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Example 4.3 Where Does The Apple Land?

• A child sits in a wagon, moving to the right
  (x-direction) at constant velocity vox. She
  throws an apple straight up (from her viewpoint)
  with initial velocity voy while she continues to
  travel forward at vox Neglect air resistance.
• Will the apple land behind the wagon, in front of
  the wagon, or in the wagon?

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Example 4.3 Cont.

• 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.

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Example 4.4 Wrong Strategy (Similar to Example
4.3 Text Book)

• 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 d away. 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 hadnt
  studied Physics yet!!)

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Example 4.4 Cont.

• 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

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Example 4.5 Thats Quite an Arm

• Non-Symmetric Projectile Motion
• Example 4.4 (text book), page 81
• 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

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Example 4.5 Cont.

• Given ?i 30º, vi 20 m/s ?
• (A) vxi vicos?i 17.3 m/s and vyi visin?i
  10.0 m/s
• At t 0 xi 0 yi 0
• Find t ? (time at which the stone hits the
  ground) with yf 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 ?

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Example 4.6 The End of the Ski Jump

• Example 4.5 (text book), page 82
• Given the figure of the ski jumper, find the
  distance d traveled along the incline.
• 1. Coordinates x and y at the end
• 2. From the figure

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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

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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 ltlt g