Vectors & Projectile Motion
Jan 21, 2016
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