Projectile Motion
Projectiles
The Range Equation
Projectile Motion
• A projectile is an object that is moving
through the air and accelerating due to
gravity
– Projectiles must be separated into their x and
y components because the motion is taking
place in 2 dimensions
• The range is the horizontal displacement
of the projectile (∆dx)
Projectile Motion - Properties
• The horizontal motion of a projectile is
constant
• The horizontal component of acceleration
of a projectile is zero (ex: viy at max height
is zero)
• Vertical acceleration is constant due to
gravity
• The horizontal and vertical components
are independent, but they share the same
time
The Equations
P.M. with No Initial Vertical Velocity
• An airplane carries relief supplies to a
motorist stranded in a snowstorm. The
pilot cannot safely land, so he has to drop
the package of supplies as he flies
horizontally at a height of 350 m over the
highway. The speed of the airplane is a
constant 52 m/s.
– Calculate how long it takes for the package to
reach the highway
– Determine the range of the package
P.M. with An Initial Vertical Velocity
• A golfer hits a gold ball with an
initial velocity of 25 m/s at an
angle of 30.0° above the
horizontal. The golfer is at an
initial height of 14 m above the
point where the ball lands.
– Calculate the maximum height of
the ball
– Determine the ball’s velocity on
landing
• Do the practice problems on page 40
The Range Equation
• If a projectile is launched and lands at the
same height as it was originally launched,
then ∆dy = 0
• We can use this information to derive the
range equation
Example – Range Equation
• Suppose you kick a soccer ball at 28 m/s
toward the goal at a launch angle of 21°.
– How long does the soccer ball stay in the air?
– Determine the distance the soccer ball would
need to cover to score a goal (the range).
• Do the practice problems on page 42
Classwork/Homework
Page 43 #’s: 2, 4, 5, 7