Warm Up 1. g = _________ 1. g = _________ Don’t forget units* Don’t forget units* 2. True or False: In a Vacuum Heavy objects fall faster than less massive ones. 2. True or False: In a Vacuum Heavy objects fall faster than less massive ones. 3. A Badger has a constant acceleration of 6 m/s 2 and an initial velocity of 3 m/s, how far will the badger go in 25 seconds? 3. A Badger has a constant acceleration of 6 m/s 2 and an initial velocity of 3 m/s, how far will the badger go in 25 seconds?

Warm Up 1. What do you think a Frame of reference is? 1. What do you think a Frame of reference is? 2. What is a Projectile? 2. What is a Projectile? 3. The back wheels of a car mysteriously fall off just as the car reaches 80 km/h, the car comes screeching to a stop 6 s later. What was the car’s acceleration? 3. The back wheels of a car mysteriously fall off just as the car reaches 80 km/h, the car comes screeching to a stop 6 s later. What was the car’s acceleration?

Reference Frame Physical object which is the basis of our coordinates. Physical object which is the basis of our coordinates. What we are basing our measurements off of. What we are basing our measurements off of.

Projectile Motion aff/hand/Projectilemotion.htm Horizontal and Vertical motions are independent.

Projectile Motion problems Step 1: Identify Variables Step 1: Identify Variables Known and unknown Known and unknown Step 2: Set up equations Step 2: Set up equations Vertical motion: Vertical motion: a = g a = g V oy = V sin θ V oy = V sin θ Horizontal Motion Horizontal Motion a = 0 a = 0 V 0x = V cos θ = V x V 0x = V cos θ = V x Step 3: Solve equations for unknowns Step 3: Solve equations for unknowns

Projectile Motion Variables V = Velocity V = Velocity V 0 = Initial velocity V 0 = Initial velocity V 0x = Initial X Velocity V 0x = Initial X Velocity V 0y = Initial Y velocity V 0y = Initial Y velocity V x = X Velocity V x = X Velocity V y = Y velocity V y = Y velocity Y = Height/Vertical position Y = Height/Vertical position θ = Launch Angle θ = Launch Angle t = time t = time g = acceleration of gravity 9.8 m/s 2 g = acceleration of gravity 9.8 m/s 2 R = Range R = Range X = Horizontal/X position X = Horizontal/X position

Remember Vertical and horizontal motions are linked by the variable time. Vertical and horizontal motions are linked by the variable time. At the initial height: y = 0 (at the beginning and end)‏ At the initial height: y = 0 (at the beginning and end)‏ At the top of the trajectory: At the top of the trajectory: V y = 0 V y = 0 t is half what it will be when the projectile returns to its initial height. t is half what it will be when the projectile returns to its initial height.

Projectile motion equations X-X 0 = V 0x * t X-X 0 = V 0x * t X-X 0 = (V 0 cos θ) * t X-X 0 = (V 0 cos θ) * t Y-Y 0 = V 0Y * t – (1/2)*g*t 2 Y-Y 0 = V 0Y * t – (1/2)*g*t 2 Y-Y 0 = (V 0 sin θ) * t – (1/2)*g*t 2 Y-Y 0 = (V 0 sin θ) * t – (1/2)*g*t 2 V y = V 0 sin θ – g*t V y = V 0 sin θ – g*t (V y ) 2 = (V 0 sin θ) 2 – 2 g (Y-Y 0 )‏ (V y ) 2 = (V 0 sin θ) 2 – 2 g (Y-Y 0 )‏

Path equation Y = (tan θ)x – (g x 2 ) / ( 2 (V 0 cos θ) 2 )‏ Y = (tan θ)x – (g x 2 ) / ( 2 (V 0 cos θ) 2 )‏ Note: this is a parabolic path Note: this is a parabolic path

Range R = (2 (V 0 ) 2 / g) * sin (2*θ)‏ R = (2 (V 0 ) 2 / g) * sin (2*θ)‏ Max range is at θ = 45 degrees Max range is at θ = 45 degrees

#41 You take a running leap off a high dive platform. You were running at 2.8 m/s and hit the water 2.6 s later. A. How high was the platform? B. How far from the edge of the platform did you hit the water?

A quarterback passes the ball with an initial velocity of 30 m/s and releases the ball at a 30 degree angle. A. Sketch the scenario. A. Sketch the scenario. B. What was the maximum height achieved by the ball? B. What was the maximum height achieved by the ball? Assume the ball is caught by the receiver at the same height it was thrown from Assume the ball is caught by the receiver at the same height it was thrown from C. How long was the ball in the air? C. How long was the ball in the air? D. How long of a completion was it? D. How long of a completion was it?

43. A pitched ball is hit by a batter at a 45 degree angle and just clears the outfield fence, 98 m away. If the fence was at the same height as the ball when it was hit, what was the velocity of the ball when it left the bat?

Homework Pg 172 (7, 19, 22, 23, 39, 40, 42, 45)‏ Have a great day!