Transcript Projectile Motion

Projectile Motion
Vocabulary
1.
2.
3.
4.
5.
Resultant
Component
Resolution
Projectile
Trajectory -The path that the projectile
follows
6. Range – pg 77
What is a PROJECTILE?
•
•
•
•
An object that is projected (launched)
It continues in motion due to its own inertia,
Is only acted upon by gravity
No force in the x-direction, only in the ydirection (gravity)
• Gravity ALWAYS acts in the y-direction, and
ONLY the y-direction
So Projectile Motion…
• Describes the motion of an object in TWO
dimensions
• We will only consider projectiles that stay
close to Earth (so ag = -9.8 m/s2)
• We will continue to disregard air resistance
Some Vocabulary…
• PROJECTILE
– The object being launched/thrown/projected
• TRAJECTORY
– The path that the projectile follows
• RANGE
– The horizontal displacement of the projectile
• MAXIMUM HEIGHT
– The vertical displacement of the projectile at the
top of its flight
The Components of Projectile Motion
• We ALWAYS break projectile motion down into
its x- and y-components
– INITIAL VELOCITY: vi
vi
• Use trigonometry to find vix and viy
– vix = vicosθ
– viy = visinθ
vix
– ACCELERATION: a
• ay = -9.8 m/s2
• ax = 0 m/s2
• Why? Think gravity and Newton’s 1st Law…
viy
Remember Freefall???
• Recall that…
– a = -9.8 m/s2, regardless if the object is moving up
or moving down
– The ONLY force acting on the object is GRAVITY
• Projectile Motion has the same conditions, and
moves in the x-direction simultaneously.
What does this look like?
• For horizontally projected objects:
• For objects projected at an angle:
VERY IMPORTANT!!!
• The components act INDEPENDENTLY of one
another!!!
• When we combine the x- and y-components,
we get the characteristic parabola-shape
– Vx remains constant (a = 0)
– Vy changes because of gravity (a = -9.8 m/s2)
How do I determine the direction?
• If an object is projected at an angle, the
direction is measured from the rightward
horizontal
To Calculate Projectile Motion…
• We use the kinematic equations
• Remember… Δd = vit + ½ at2
– RANGE (x-displacement) uses x-components and total
time
• Δdx = vixttotal + ½ axttotal2 = vixttotal
• Remember that a = 0 in the x-direction
– HEIGHT (y-displacement) uses y-components
• Δdy = viyt + ½ ayt2
• Remember that a = -9.8 m/s2 in the y-direction
More on Calculations
• ay = (vfy2 – viy2) / 2Δdy
– (to find max height)
• ay = (vfy – viy) / t
– (to find time to max height)
• These only apply in the y-direction (vx doesn’t
change)
• ay = -9.8 m/s2 ALWAYS
• Remember, at the top of its path, a projectile’s
vy = 0 (so vfy = 0)
EXAMPLES
• A cannonball is fired from a cannon at an
angle of 32° and an initial velocity of 54 m/s.
A. What are the components of the initial velocity?
B. How long does it take the cannonball to reach
maximum height?
C. What is the cannonball’s maximum height?
D. What is the total time of travel?
E. What is the cannonball’s range?
A cannonball is fired from a cannon at an angle of
32 ° and an initial velocity of 54 m/s.
A. What are the components of the initial
velocity?
A cannonball is fired from a cannon at an angle of
32 ° and an initial velocity of 54 m/s.
B. How long to maximum height?
A cannonball is fired from a cannon at an angle of
32 ° and an initial velocity of 54 m/s.
C. What is the maximum height?
A cannonball is fired from a cannon at an angle of
32 ° and an initial velocity of 54 m/s.
D. What is the total time?
A cannonball is fired from a cannon at an angle of
32 ° and an initial velocity of 54 m/s.
E. What is the range?