Kinematics in Two Dimensions
description
Transcript of Kinematics in Two Dimensions
![Page 1: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/1.jpg)
Kinematics in Two Dimensions
Chapter 3
![Page 2: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/2.jpg)
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?
![Page 3: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/3.jpg)
ttt o
o
rrrv
Average velocity is the displacement divided by the elapsed time.
![Page 4: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/4.jpg)
tt
rv
0
lim
![Page 5: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/5.jpg)
The instantaneous velocity indicates how fastthe car moves and the direction of motion at eachinstant of time.
tt
rv
0
lim
![Page 6: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/6.jpg)
TGPTPG vvv
![Page 7: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/7.jpg)
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?
![Page 8: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/8.jpg)
sm5.4
sm0.2sm0.4 2222
WSBWBS vvv
WSBWBS vvv
630.20.4tan 1
s 450sm4.0
m 1800t
![Page 9: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/9.jpg)
ttt o
o
vvva
DEFINITION OF AVERAGE ACCELERATION
ov
vv
![Page 10: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/10.jpg)
Equations of Kinematics – know by heart!
tvvx o 21
221 attvx o
atvv o
axvv o 222
![Page 11: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/11.jpg)
Projectiles
• Projectiles move in 2 directions:1) HORIZONTALLY – CONSTANT
VELOCITY2) VERTICALLY – FREE-FALL (CONSTANT
ACCELERATION)3) AIR RESISTANCE IS NEGLIGIBLE IN
EACH CASE
![Page 12: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/12.jpg)
![Page 13: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/13.jpg)
Under the influence of gravity alone, an object near the surface of the Earth will accelerate downwards at 9.80m/s2.
2sm80.9ya 0xa
constant oxx vv
HORIZONTAL LAUNCH
For a horizontally launched projectile,
![Page 14: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/14.jpg)
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
![Page 15: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/15.jpg)
Given U Equations / Substitutions SolutionHorizontal Vertical
![Page 16: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/16.jpg)
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?
![Page 17: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/17.jpg)
Lab
• “Hunger Games”.
![Page 18: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/18.jpg)
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.
![Page 19: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/19.jpg)
ov
oxv
oyv
sm1440sinsm22sin ooy vv
![Page 20: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/20.jpg)
Given U Equations / Substitutions SolutionHorizontal Vertical
![Page 21: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/21.jpg)
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?
![Page 22: Kinematics in Two Dimensions](https://reader034.fdocuments.in/reader034/viewer/2022051020/568160ae550346895dcfcf0a/html5/thumbnails/22.jpg)
Rocket Lab