Vectors & Projectile Motion

Motion is Relative

►Frame of Reference - perspective from which you observe

Truck 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 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 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?

►Scalar - measurement of magnitude

only

Ex) mass, volume, speed

►Vector - measurements with both

magnitude and direction

Ex) velocity, acceleration, force

arrowhead = direction length of arrow = magnitude

Vectors

Vector addition

Resultant – sum of vectors

Pythagorean Theorem

a2 + b2 = c2

► c2 = a2 + b2

► c2 = 802 + 602 ► c2 = 6400 + 3600 ► √c2 = √10,000► c = 100 km/hr

EX) What is the resultant vector for 4 km/hr north and 3 km/hr

east?

► c2 = a2 + b2

► c2 = 42 + 32

► c2 = 16 + 9

► c2 = 25► c = 5

km/h

►Boat crossing river animation…http://www.schulphysik.de/suren/Applets.html

Vector addition

► Pythagorean Theorem -

► Parallelograms -

► Head-to-tail method -

► Trigonometry -

What is the vertical and horizontal component of a

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

SOH-CAH-TOA

Ex) What are the horizontal and vertical components of the

following vector?

3634sin

y

3634cos

x

my 20

mx 30

Projectile Motion

Projectile – an object moving through air affected by gravity

Projectile Demos

►Shooter/ Dropper►Monkey and Hunter

Projectile Motion Horizontal and vertical motion act

independently

vtdx 2

2

1atd y

How fast is the ball thrown?

►Vertical►d= .5at2

►5 = .5(10)t2

►t= 1 second

►Horizontal►v= d/t►v= 20m/1s►v= 20 m/s

The ball is thrown at 20 m/s!

What angle should a ball be kicked to get the

farthest?

Upwardly-Moving Projectiles

Projectiles launched at the same speed but different

angles.

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

You are already off the ground 1-2 meters.

45º is not the ideal angle for high speed projectiles either. Why?

Air resistance must be considered.

Fast Moving Projectiles

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

Fast Moving Projectiles

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

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

Hang Time

This type of problem is more difficult…

► http://physicsquest.homestead.com/quest3n.html ► http://www.mesacc.edu/~

scotz47781/mat120/notes/projectile_motion/projectile_motion.html