Projectile Motion I 11/7/14

Throwing 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 air The velocity changes. The acceleration is constant, it stays the same 9.81 m/s/s, downward throughout the flight.

Projectiles Projectiles: are objects where gravity and air resistance are the only forces acting Projectiles travel with a parabolic trajectory (path)

Projectiles 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 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 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

Components Component: the projection of a vector quantity along a perpendicular axis

Components Horizontal Right = +x Left = -x Vertical Up = +y Down = -y

Projectile Quantities Displacement (m) x = horizontal displacement y = vertical displacement Velocity (m/s) v x = horizontal velocity v y = vertical velocity

Projectile Quantities Acceleration a x = 0 m/s 2 (no horizontal acceleration) a y = m/s 2 or “g” Time (s) t = time - Does not depend on direction (scalar) - It is the same for horizontal and vertical components

Projectiles and Time (i.e.) A projectile has the same time for how long it goes up and/or down AND left or right

Mythbusters Dropped vs. Fired Bullet

Projectile Motion II 11/10/14

Quantity Horizontal Component Vertical Component Displacement Yes, same distance each second Yes, different distances each second. Velocity Yes, Constant Yes, changing by m/s each second. AccelerationNo Yes, 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 TimeHorizontal Displacement Vertical Displacement 0 s0 m, right0 m 1 s20 m, right5 m, down 2 s40 m, right20 m, down 3 s60 m, right45 m, down 4 s80 m, right80 m, down 5 s100 m, right125 m, down

Velocity TimeHorizontal Velocity Vertical Velocity 0 s20 m/s, right0 m/s 1 s20 m/s, right10 m/s, down 2 s20 m/s, right20 m/s, down 3 s20 m/s, right30 m/s, down 4 s20 m/s, right40 m/s, down 5 s20 m/s, right50 m/s, down

Acceleration TimeHorizontal Acceleration Vertical Acceleration 0 s0 m/s/s10 m/s/s, down 1 s0 m/s/s10 m/s/s, down 2 s0 m/s/s10 m/s/s, down 3 s0 m/s/s10 m/s/s, down 4 s0 m/s/s10 m/s/s, down 5 s0 m/s/s10 m/s/s, down

A Falling Object

A falling object

Projectile (Horizonal)

Projectile (Launched)

Projectile Graph Graph Due Wed. 11/12/14

Projectile Graph Graph Due Wed. 11/12/14

Projectile Motion III 11/12/14

Projectile Equations

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 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 1 st ) is a scalar, it is the same for the horizontal and vertical components

Projectile Problems 2 Types of problems: – “Horizontally” from a height – “Launched” from the ground

Projectile “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?