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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o

rrrv

Average velocity is the displacement divided by the elapsed time.

tt

rv

0

lim

The instantaneous velocity indicates how fastthe car moves and the direction of motion at eachinstant of time.

tt

rv

0

lim

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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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vv

Equations of Kinematics – know by heart!

tvvx o 21

221 attvx o

atvv o

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

oyv

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