Transcript Projectile Motion - Eleanor Roosevelt High School

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
Projectile Motion
The ball is in free fall vertically and moves at
constant speed horizontally!!!
Projectile Motion
Projectile Motion
Projectile Motion
Projectile Motion
Projectile Motion
y
Horizontal (x)
dx  vxt
Vertical (y)
1 2
dy  vi t  gt
2
v y  vi  gt
y
y
x
Projectile Motion
• What happens when we add air resistance?
• Adds a new force on the ball
• The force is in the opposite direction to the
ball’s velocity vector and is proportional to
the velocity at relatively low speeds
• Need calculus to sort out the resulting
motion
• Lowers the angle for maximum range
Projectile Motion
• The trick to maximum range is just to keep
the object off the ground for as long as
possible.
• This allows the horizontal motion to be a
maximum since dx = vxt
• Make range longer by going higher for your
starting point
• Make range longer by having more velocity
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!!!
The Moon
• Distance is about 240,000 miles
• Takes 27.3 days to make an orbit
Elliptical Orbits
• Give the object a speed a bit greater than 8
km/sec and the orbit will be elliptical
Elliptical Orbits
Elliptical Orbits
Sum of distances from foci to point on the
ellipse is a constant!!!
Kepler’s Laws
• Each planet moves in an elliptical orbit with
the sun at one focus of the ellipse.
• The line from the sun to any planet sweeps
out equal areas of space in equal time
intervals
• The squares of the periods of the planets are
proportional to the cubes of their average
distances from the sun
Kepler’s Laws
Energy Conservation
Energy Conservation
Energy Conservation
Escape Speed
Throw at > 11.2
km/sec and ball
escapes the pull
of the earth!!!