Projectile Motion

Projectile Motion Motion in 2-Dimensions Any object which the only force is gravity Three types of Projectiles: 1. Dropped 2. thrown vertically 3. thrown at angle

Trajectory => Parabolic Path!!!

The trajectory of a projectile (due to gravity) Projectile motion is a combination of HORIZONTAL and VERTICAL motions. Horizontal motion is independent of its vertical motion Projectiles have symmetric paths.

Lets look at the 2 motions of a Projectile separtaely Horizontal Vertical NO horizontal forces acting Force of Gravity NO horizontal acceleration Vertical acceleration due to gravity Horizontal velocity is constant -(9.8 m/s2) Horizontal motion is independent of its vertical motion

Projectile Motion Webhunt 3.

Newton’s First Law of Motion An object at rest tends to stay at rest and an object in motion tends to stay in constant motion (with the same speed and in the same direction) UNLESS acted upon by an unbalanced force.

Newton’s 1st Law: An object in motion remains in motion... Inertia cart demo

Inertia An object in motion (the moon) will continue in motion at a constant speed Orbiting the earth

1. Where will the cannonball land when it is shot out of the truck that is moving at a constant velocity? An object in motion (the truck AND the ball) will continue in motion with the SAME constant velocity…

Projectile Horizontal & vertical direction are INDEPENDENT of one another. DOES NOT

Projectile Horizontal Vertical Horizontal motion is independent of its vertical motion Q: What is present to speed up or slow down the object? Q: What is present to speed up or slow down the object? Nothing pushing or pulling it Gravity pulling downward No horizontal acceleration Vertical acceleration due to gravity Horizontal velocity is constant (9.8 m/s2) Range: d = v * t “How Far” d = ½ g t2

0m 5m 10m 15m 20m 25m 30m 35m 40m 45m 50m 55m 60m 65m I I I I I I I I I I I I I I Cliff 0m __ 5m __ 10m __ 15m __ 20m __ 25m __ 30m __ 35m __ 40m __ 45m __ 50m __ 55m __ 60m __ 65m __ 70m __ 75m __ 80m __ 85m __ 90m __ 95m __ 100m _

If the car drove off the cliff with a velocity of 12 m/s, fill in the table below for the horizontal motion of the car at each time.

Fill in the table below for the vertical motion of the car

Projectile Motion Webhunt

Projectile COMBINE the horizontal travel and the vertical travel (due to gravity) and the result is a parabolic path Horizontal motion is independent of its vertical motion

Compare the horizontal TIME and the vertical free-fall TIME 1 s 2 s 3 s 4 s 5 s 1 s 1 s 2 s 2 s In 1 sec. the ball moves horizontally AND falls vertically at the same time. 3 s 3 s 4 s 4 s

Projectile BOTH objects will fall at the same rate (acceleration of gravity 9.8m/s2) The velocity it has in the horizontal motion does not affect or change or depend on the velocity and acceleration in the vertical direction.

Demo: Ball Dropped vs. Ball Fired https://www.youtube.com/watch?v=tF_zv3TCT1U Mythbusters: bullet dropped vs bullet fired. (3 min)

Plane and the Package Where does the package land relative to the plane?? When did it drop the package Describe the HORIZONTAL VELOCITY of the package

Projectile Horizontal Vertical t = d v The TIME is the SAME! t How Long time it traveled: How Long of time of free-fall : t = d v t

(time from maximum height to ground) Projectile Motion horizontal motion is INDEPENDENT of vertical motion Horizontal motion is independent of its vertical motion Horizontal Vertical How Far (“Range”): How Far (high): d = v * t h = ½ g t2 How Long: t = d v t = √((2*h)/g) How Fast: Vfy = g*t v = d t (time from maximum height to ground) V

Step 2: Add “g= 9.8 m/s2” to the vertical given. Step 1: Put the two “givens” in the proper place (horizontal or vertical) Step 2: Add “g= 9.8 m/s2” to the vertical given. Step 3: Solve for TIME! (using either horizontal or vertical, which ever one has two given) Step 4: Use the time to solve for the other unknown. Horizontal Given Unknown Equation Solve Solution   Vertical Unkown

If a cannonball is fired off a cliff at a horizontal velocity of 100 m/s and hits the ground 85 m away from the cliff… Predict: 1. The TIME required for the cannonball to hit the ground. 2. The vertical velocity of the cannon ball when it hits the ground. Gx (Horizontal) U E S Gy (Vertical)

A team of IPC students are in a plane 200 m above the ground and traveling at 30 m/s. They needed to hit a target on the ground with a water balloon in order to earn an A+… Predict: 1. The time required for the water balloon to hit the ground. 2. How far away should they drop their water balloon in order to hit the target? Gx U E S Gy

A bullet traveling horizontally at 800 m/s hits a target 180 m away A bullet traveling horizontally at 800 m/s hits a target 180 m away. How far does the bullet fall before hitting the target? Predict: 1. The time required for the bullet to hit the target. 2. How far does the bullet fall before hitting the target? Gx U E S Gy

Projectile Simulator (if time) http://phet.colorado.edu/sims/projectile-motion/projectile-motion_en.html Path of a projectile with and without air resistance

Projectile Angle vs. Range Which cannon angle will launch the cannonball the FARTHEST range?

The 45° angle launched the ball the farthest The 45° angle launched the ball the farthest. How does the range distance of the 30° and 60° angle compare?

Projectile Motion at an Angle What is the SUM of the angles that land at the SAME distance (range)? 75° + 15° = 90° 60° + 30° = 90°