Throwing a ball in the airThrowing a ball in the air
• On the way up:
• At the top of the throw:
• On the way down:
• velocity decreases • acceleration stays the
same.• velocity zero • acceleration stays the
same.• velocity increases • acceleration stays the
same.
Throwing a ball in the airThrowing a ball in the air
• The velocity changes.
• The acceleration is constant, it stays the same 9.81 m/s/s, downward throughout the flight.
ProjectilesProjectiles
• Projectiles: are objects where gravity and air resistance are the only forces acting
• Projectiles travel with a parabolic trajectory (path)
ProjectilesProjectiles
• A projectile’s horizontal component is independent of the vertical component
• The force of gravity does not affect the horizontal component of motion
• (i.e.) What is happening left and right does not effect what is happening up and down
Air ResistanceAir Resistance
• Air Resistance: A force of friction that acts on an object moving through the air
• For projectile motion we will often neglect or assume that air resistance is extremely small
Projectile TermsProjectile Terms
• Range: The distance a projectile travels horizontally from the initial position.
• Max Height: The greatest distance a projectile travels vertically
• Hang Time: The total amount of time a projectile is in the air
Projectile QuantitiesProjectile Quantities
• Displacement (m)
x = horizontal displacement
y = vertical displacement
• Velocity (m/s)
vx = horizontal velocity
vy = vertical velocity
Projectile QuantitiesProjectile Quantities• Acceleration
ax = 0 m/s2 (no horizontal acceleration)
ay = -9.80 m/s2 or “g”
• Time (s)
t = time
- Does not depend on direction (scalar)
- It is the same for horizontal and vertical components
Projectiles and TimeProjectiles and Time
• (i.e.) A projectile has the same time for how long it goes up and/or down AND left or right
Quantity HorizontalComponent
Vertical Component
DisplacementYes,
same distanceeach second
Yes, different
distances each second.
VelocityYes,
ConstantYes, changing by -9.81 m/s each second.
Acceleration NoYes, constant
9.81 m/s/s, downward
“g”
Projectile Example
•What happens to a projectile’s horizontal and vertical displacement, velocity and acceleration?
•Example: An object with a initial horizontal velocity of 20 m/s to the right and vertical velocity of 0 m/s.
Displacement
Time HorizontalDisplacement
VerticalDisplacement
0 s 0 m, right 0 m
1 s 20 m, right 5 m, down
2 s 40 m, right 20 m, down
3 s 60 m, right 45 m, down
4 s 80 m, right 80 m, down
5 s 100 m, right 125 m, down
Velocity
Time HorizontalVelocity
VerticalVelocity
0 s 20 m/s, right 0 m/s
1 s 20 m/s, right 10 m/s, down
2 s 20 m/s, right 20 m/s, down
3 s 20 m/s, right 30 m/s, down
4 s 20 m/s, right 40 m/s, down
5 s 20 m/s, right 50 m/s, down
Acceleration
Time HorizontalAcceleration
VerticalAcceleration
0 s 0 m/s/s 10 m/s/s, down
1 s 0 m/s/s 10 m/s/s, down
2 s 0 m/s/s 10 m/s/s, down
3 s 0 m/s/s 10 m/s/s, down
4 s 0 m/s/s 10 m/s/s, down
5 s 0 m/s/s 10 m/s/s, down
Remember RIDGES (10/20)Remember RIDGES (10/20)
• R – Read the problem carefully!• I – Identify what you are looking for and the
Information that is given. (1 & 2 in T-Chart)
• D – Draw a picture of the problem.• G – Generate a plan (T-Chart)• E – Evaluate the Equation(s) that can help
solve the problem (3 T-Chart)• S – Solve the problem and answer with the
appropriate units (4 & 5 in T-Chart)
Projectile ProblemsProjectile Problems
1. Draw a sketch of the problem to determine horizontal and vertical components
2. Use a T-Chart to organize the problem
3. Time (often needed to be solved for 1st) is a scalar, it is the same for the horizontal and vertical components
Projectile ProblemsProjectile Problems
• 2 Types of problems:
– “Horizontally” from a height
– “Launched” from the ground
Projectile “Horizontal” ExampleProjectile “Horizontal” Example
• A tennis ball rolls off a lab bench that is 1.1 m high with a horizontal velocity of 3.7 m/s.
• a) How long will it be in the air for?• b) How far from the table does it land?• c) What is the ball’s vertical velocity as
it hit the ground?• d) What is the ball’s resultant velocity
as it hits the ground?