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**Kinematics in Two Dimensions**

Chapter 3 Kinematics in Two Dimensions

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GT Homework 2012 The treasure map in the figure gives the following directions to the buried treasure: “Start at the old oak tree, walk due north for 540 paces, then due east for 110 paces. Dig.” But when you arrive, you find an angry dragon just north of the tree. To avoid the dragon, you set off along the yellow brick road at an angle 60o EN. After walking 400 paces you see an opening through the woods. In which direction and how far do you need to go to get to the treasure from there?

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**Average velocity is the**

displacement divided by the elapsed time.

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**The instantaneous velocity indicates how fast**

the car moves and the direction of motion at each instant of time.

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**Example 11 Crossing a River**

The engine of a boat drives it across a river that is 1800m wide. The velocity of the boat relative to the water is 4.0m/s directed perpendicular to the current. The velocity of the water relative to the shore is 2.0m/s. (a) What is the velocity of the boat relative to the shore? (b) How long does it take for the boat to cross the river?

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**DEFINITION OF AVERAGE ACCELERATION**

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**Equations of Kinematics – know by heart!**

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**Projectiles Projectiles move in 2 directions:**

HORIZONTALLY – CONSTANT VELOCITY VERTICALLY – FREE-FALL (CONSTANT ACCELERATION) AIR RESISTANCE IS NEGLIGIBLE IN EACH CASE

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HORIZONTAL LAUNCH Under the influence of gravity alone, an object near the surface of the Earth will accelerate downwards at 9.80m/s2. For a horizontally launched projectile,

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A Falling Care Package The airplane is moving horizontally with a constant velocity of +115 m/s at an altitude of 1050m. Determine its horizontal displacement from the place of the drop

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**Equations / Substitutions**

Given U Equations / Substitutions Solution Horizontal Vertical

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**Conceptual Example 5 I Shot a Bullet into the Air... **

3.3 Projectile Motion Conceptual Example 5 I Shot a Bullet into the Air... Suppose you are driving a convertible with the top down. The car is moving to the right at constant velocity. You point a rifle straight up into the air and fire it. In the absence of air resistance, where would the bullet land – behind you, ahead of you, or in the barrel of the rifle?

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Lab “Hunger Games”.

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**Example 6 The Height of a Kickoff **

3.3 Projectile Motion Example 6 The Height of a Kickoff A placekicker kicks a football at and angle of 40.0 degrees and the initial speed of the ball is 22 m/s. Ignoring air resistance, determine the maximum height that the ball attains.

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**Equations / Substitutions**

Given U Equations / Substitutions Solution Horizontal Vertical

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**Conceptual Example 10 Two Ways to Throw a Stone**

From the top of a cliff, a person throws two stones. The stones have identical initial speeds, but stone 1 is thrown downward at some angle above the horizontal and stone 2 is thrown at the same angle below the horizontal. Neglecting air resistance, which stone, if either, strikes the water with greater velocity?

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Rocket Lab

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