Transcript Projectile Motion

Projectile Motion
The motion of a falling object with air
resistance and gravity acting on it
Projectiles
• A projectile is any object upon which the only
force is gravity
• Projectiles travel with a parabolic trajectory
due to gravity
• There are no horizontal forces and no
horizontal acceleration on projectiles
Projectiles
• The horizontal velocity of a projectile is
constant
• The vertical acceleration of a projectile is
caused by gravity and is 9.8m/s/s down
• The horizontal and vertical motion of a
projectile are independent of each other
Projectile Motion
• A force is not required to keep an object in
motion
• A force is required to maintain acceleration
• If a projectile is moving upward there is a
downward force and downward acceleration
• The object is moving upward and slowing
down
Gravity and vertical acceleration
• Gravity only causes a vertical acceleration
• Gravity does not affect the horizontal distance
or motion an object travels
• Gravity will affect the vertical distance and
motion of an object only
Horizontally launched projectiles
• There has to be a horizontal force to cause a
horizontal acceleration
• A projectile has a constant horizontal velocity
and a downward vertical acceleration
(deceleration)
Horizontal Projectiles
Horizontal Motion
Vertical Motion
Forces
No
Yes, gravity
Acceleration
No
Velocity
Constant
Yes, gravity at
9.8m/s/s
Changing by 9.8m/s
each second
Non-Horizontally Launched Projectiles
• When the projectile is launched at an angle the
path is a parabola
• If there was no gravity the projectile would
continue upward
•
no gravity
•
gravity
Vertical Displacement
• The vertical displacement of an object can be
calculated using:
•
y = .5 * g * t2 (* = multiplied by)
y = vertical displacement
g = gravity at -9.8m/s/s
t = time in seconds
• Use this equation when an object is dropped
from rest – it has no initial vertical velocity
Horizontal Displacement
• The horizontal displacement of a projectile
can be calculated using the following:
x = vix * t
where x = horizontal displacement in m
vix = initial horizontal velocity in m/s
t = time in s
In this case there is no initial vertical velocity, since
the projectile is launched horizontally
Vertical Displacement of an AngledLaunched Projectile
• To calculate the vertical displacement of a
projectile launched at an angle
•
y = viy * t + 0.5 * g * t2
•
y= vertical displacement in m
viy = initial velocity in m/s
t = time in s
g = gravity, -9.8 m/s/s
t = time in s
Sample Problem
• A projectile has an initial velocity viy of 19.6m/s
and a horizontal velocity of 33.9m/s, what is the
vertical and horizontal displacement after 1 s?
y = viy * t + 0.5 * g * t2
y = (19.6m/s) x (1s) + 0.5 x (-9.8m/s/s) x (1s)2
y = 19.6m/s + (-4.9m)
y = 14.7m (vertical displacement)
x = vix * t
x = (33.9m/s) x (1s)
x = 33.9m (horizontal displacement)