Notes: Projectile Motion

Projectiles are... Objects thrown or launched into the air Objects thrown or launched into the air While in the air, gravity is the only force acting on them While in the air, gravity is the only force acting on themExamples:Footballs Angry Birds Kids who ride bikes off cliffs Kids who ride bikes off cliffs

Projectiles have 2 components to their motion... Vertical acceleration due to gravity Vertical acceleration due to gravity Constant Horizontal Speed (0 acceleration) Constant Horizontal Speed (0 acceleration)

This horizontal velocity also has no acceleration – it is constant speed This horizontal velocity also has no acceleration – it is constant speed θ V Range = horizontal distance traveled

How do we deal with them? Set up a double T-charts Set up a double T-charts X Y vfvf v0v0 a t d

What will the acceleration be? X Y vfvf v0v0 a t d -9.8m/s 2 0 m/s 2 Same v 0 & v f same How will the times compare?

When launched at an angle Look at it like a right triangle, with the initial velocity as the hypotenuse. Look at it like a right triangle, with the initial velocity as the hypotenuse. Find the x and y components of the v 0 Find the x and y components of the v 0 θ VxVx V y0 V0V0 X Y vfvf v0v0 a t d -9.8m/s 2 0 m/s 2

When asked for maximum height Only half of the time has passed Only half of the time has passed θ V Max Height ½ time in the air = max height

Other important information: For all of our problems we ignore friction – which can affect path shape and motion For all of our problems we ignore friction – which can affect path shape and motion Projectile motion is a parabola shape Projectile motion is a parabola shape Trajectories of 45° will have the greatest height and range Trajectories of 45° will have the greatest height and range At max. height vertical v = 0m/s At max. height vertical v = 0m/s Initial velocity and final velocity are the same, but in different directions Initial velocity and final velocity are the same, but in different directions

Projectiles launched horizontally Cliff This is just a drop with forward motion added. This is just a drop with forward motion added. Vertical v i = 0m/s Y vfvf vivi 0 a -9.8 t y x vfvf vivi a0 t x

Example 1: A bike is ridden off of a 25 m cliff at 15 m/s. Solve for everything!!! A bike is ridden off of a 25 m cliff at 15 m/s. Solve for everything!!!

Example 2: A boy shoots a slingshot horizontally off a cliff at 20 m/s. It lands 100 m from the base of the cliff. Solve for everything!!! A boy shoots a slingshot horizontally off a cliff at 20 m/s. It lands 100 m from the base of the cliff. Solve for everything!!!