Ch 3. Kinematics in Two Dimensions Average velocity instantaneous velocity 1.
Kinematics in Two Dimensions
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Transcript of Kinematics in Two Dimensions
Kinematics in Two Dimensions
Chapter 3
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 fastthe car moves and the direction of motion at eachinstant 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 relativeto 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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s 450sm4.0
m 1800t
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DEFINITION OF AVERAGE ACCELERATION
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Equations of Kinematics – know by heart!
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221 attvx o
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axvv o 222
Projectiles
• Projectiles move in 2 directions:1) HORIZONTALLY – CONSTANT
VELOCITY2) VERTICALLY – FREE-FALL (CONSTANT
ACCELERATION)3) AIR RESISTANCE IS NEGLIGIBLE IN
EACH CASE
Under the influence of gravity alone, an object near the surface of the Earth will accelerate downwards at 9.80m/s2.
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constant oxx vv
HORIZONTAL LAUNCH
For a horizontally launched projectile,
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
Given U Equations / Substitutions SolutionHorizontal Vertical
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 pointa rifle straight up into the air and fire it. In the absence of airresistance, where would the bullet land – behind you, aheadof you, or in the barrel of the rifle?
Lab
• “Hunger Games”.
3.3 Projectile Motion
Example 6 The Height of a Kickoff
A placekicker kicks a football at and angle of 40.0 degrees andthe initial speed of the ball is 22 m/s. Ignoring air resistance, determine the maximum height that the ball attains.
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oxv
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sm1440sinsm22sin ooy vv
Given U Equations / Substitutions SolutionHorizontal Vertical
Conceptual Example 10 Two Ways to Throw a Stone
From the top of a cliff, a person throws two stones. The stoneshave identical initial speeds, but stone 1 is thrown downwardat some angle above the horizontal and stone 2 is thrown atthe same angle below the horizontal. Neglecting air resistance,which stone, if either, strikes the water with greater velocity?
Rocket Lab