Vectors & Vectors & Projectile Projectile MotionMotion

Physics LGPhysics LG

Jan. 30, 2009Jan. 30, 2009

Motion is Motion is RelativeRelative

►Frame of ReferenceFrame of Reference - perspective from - perspective from which you observe which you observe

Truck at RestTruck at Rest

If the ball is thrown at 60 km/h relative to the truck, at what velocity

will the person catch the ball at?

Truck Moving AwayTruck Moving Away

► If the ball is thrown at 60 km/h west relative to the truck and the truck moves at 40 km/h east relative to the catcher, at what velocity will the person catch the ball at?

Truck Moves TowardsTruck Moves Towards

► If the ball is thrown at 60 km/h west relative to the truck and the truck moves at 40 km/h west relative to the catcher, at what velocity will the person catch the ball at?

►ScalarScalar - measurement of magnitude - measurement of magnitude

onlyonly

Ex) mass, volume, speedEx) mass, volume, speed

►VectorVector - measurements with both - measurements with both

magnitude and direction magnitude and direction

Ex) velocity, acceleration, forceEx) velocity, acceleration, force

arrowhead = directionarrowhead = direction length of arrow = magnitudelength of arrow = magnitude

Vectors Vectors

Vector addition Vector addition

ResultantResultant – sum of vectors – sum of vectors

Pythagorean TheoremPythagorean Theorem

aa22 + b + b22 = c = c22

► cc22 = a = a22 + b + b22

► cc22 = 80 = 8022 + 60 + 6022 ► cc22 = 6400 + 3600 = 6400 + 3600 ► √ √cc22 = √10,000 = √10,000► c = 100 km/hrc = 100 km/hr

Example ProblemExample Problem

► cc22 = a = a22 + b + b22

► cc22 = 4 = 422 + 3 + 322 ► cc22 = 16 + 9 = 16 + 9► cc22 = 25 = 25► c = 5 km/hc = 5 km/h

Vector additionVector addition

► Pythagorean Theorem - Pythagorean Theorem -

► Parallelograms - Parallelograms -

► Head-to-tail method - Head-to-tail method -

► Trigonometry -Trigonometry -

Vector AdditionVector Additionhttp://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=51http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=51

What is the vertical and What is the vertical and horizontal component of a horizontal component of a

vector? vector? http://www.batesville.k12.in.us/Physics/APPhyNet/Vectors/Hor_&_Vert_Comps.html

Projectile MotionProjectile Motion

ProjectileProjectile – an object moving through – an object moving through air affected by gravity air affected by gravity

Projectile DemosProjectile Demos

►Shooter/ DropperShooter/ Dropper►Monkey and HunterMonkey and Hunter

Projectile MotionProjectile Motion Horizontal and vertical motion act independentlyHorizontal and vertical motion act independently

vtdx 2

2

1atd y

How fast is the ball thrown?How fast is the ball thrown?

►VerticalVertical►d= .5atd= .5at22

►5 = .5(10)t5 = .5(10)t22

►t= 1 secondt= 1 second

►HorizontalHorizontal►v= d/tv= d/t►v= 20m/1sv= 20m/1s►v= 20 m/sv= 20 m/s

The ball is thrown at 20 m/s!

What angle What angle should a ball be should a ball be kicked to get the kicked to get the

farthest?farthest?

Upwardly-Moving ProjectilesUpwardly-Moving Projectiles

Projectiles launched at the Projectiles launched at the same speed but different same speed but different

angles. angles.

Shot Put - 45º is not the ideal angle, Shot Put - 45º is not the ideal angle,

why?why? You are already off the ground 1-2 You are already off the ground 1-2

meters.meters.

45º is the ideal angle for high speed 45º is the ideal angle for high speed projectiles either. Why? projectiles either. Why?

Air resistance must be considered. Air resistance must be considered.

Fast Moving ProjectilesFast Moving Projectiles

►What would happen if you threw a ball so What would happen if you threw a ball so fast that the curvature of the earth came fast that the curvature of the earth came into play?into play?

Fast Moving ProjectilesFast Moving Projectiles

► Satellite- a projectile traveling fast enough Satellite- a projectile traveling fast enough to fall around the earth rather than intoto fall around the earth rather than into

► To stay in orbit around the earth, a satellite To stay in orbit around the earth, a satellite needs to travel at 8 km/s!needs to travel at 8 km/s!

Hang TimeHang Time

Due Next Week POTW 11s Bull’s eye lab 12s Rocket Lab 30s Motion Worksheet #1 31s Motion Worksheet #2 32s Motion Review Test will be next Thursday Feb 5th

►Study the 1s, 2s, labs, and worksheets►Use the back page of booklet under motion for note sheet for test.