Physics Day 33

LO: recognize the independence of the horizontal and vertical components of motion

AGENDADo Now

Project

HW#6Pr. 1-3

on page 99

Professional basketball player “Kiwi” has a hang time of 2.25 seconds with a 30 degree launch angle. 1) How long does it take to reach his maximum height?2) What is the maximum height?3) Are these numbers reasonable?

What is a projectile?• A projectile is any object that once projected or dropped

continues in motion by its own weight and is influenced only by the downward force of gravity.

• a projectile is any object upon which the only force is gravity.

•  

Projectile Motion

• Describe the motion of an object in TWO dimensions

• Keep it simple by considering motion close to the surface of the earth for the time being

• Neglect air resistance to make it simpler

The Plane and The PackageIn the course of its flight, the plane drops a package from its luggage compartment. What will be the path of the package and where will it

be with respect to the plane?

Characteristics of a Projectile's Trajectory

• There are the two components of the projectile's motion - horizontal and vertical motion.

• the projectile travels with a constant horizontal velocity and a downward vertical acceleration.

• And since perpendicular components of motion are independent of each other, these two components of motion can (and must) be discussed separately.

HorizontalMotionVerticalMotion

• Horizontal• Motion• Vertical• Motion• Forces• (Present? - Yes or No) (If present, what dir'n?)

• No• Yes The force of gravity acts downward

• Acceleration• (Present? - Yes or No) (If present, what dir'n?)

• No• Yes "g" is downward at 9.8 m/s/s

• Velocity• (Constant or Changing?)• Constant• Changing (by 9.8 m/s each second)

Where should the zookeeper aim her banana cannon

to successfully hit the monkey?

Projectile Motion

The ball is in free fall vertically and moves at constant speed horizontally!!!

Projectile Motion

Examples

• A projectile is fired horizontally from a cliff44.1 meter high at an initial velocity of 50 m/s.

• 1) How long after it is fired does it hit the ground?• 2) How far away from the cliff does it hit the

ground?• 3) What it its vertical velocity as it hits the

ground?

Examples

• 2. Ima Peode wishes to throw a 2.8kg pumpkin horizontally of the top of the school roof (which is 10.4meter) in order to hit Mr. K Who stands a distance of 13.4m away from the base of the building. What is the initial velocity must be in order to hit Mr. K?

Projectile Motion

Projectile Motion

Projectile Motion

Projectile Motion

Projectile Motion

x

y

gtvv

gttvd

tvd

iyy

yiy

xx

2

2

1

(y) Vertical

(x) Horizontal

Projectile Motion

Satellites

• Curvature of the earth enters into our calculations

If I start 5 m above the surface, it will still be at 5 m after one second if it is moving 8000 m/sec

Satellites

Throw at 8000 m/sec

This is about 18,000 mph

Earth circumference is 25,000 miles

Takes 25000/18000 = 1.4 hours = 84 minutes

Higher altitude longer

Satellites

Force of gravity on bowling ball is at 90o to velocity, so it doesn’t change the velocity!!!

If no air resistance, gravity doesn’t change speed of satellite, only direction!!!

Communications Satellites

• Farther out you go, the bigger the circumference of the orbit

• It takes longer for the trip

• Also, gravity weakens by inverse square law the farther out you go

• Make the distance so that it takes 24 hours for the orbit

• Satellite is stationary in the sky!!!

Escape Speed

Throw at > 11.2 km/sec and ball escapes the pull of the earth!!!