Unit 3: Projectile Motion Here is a look at what will be studying this unit (Trailer)

IV. Tossing a Ball up in the Air 0 m/s (comes to a rest) time to fall back to original position speed at original position on the way down

I. Projectile Fired Straight Up t = 4 s, v = 0 m/s → ← t = 5s, v = -10 m/s t = 3 s, v = +10 m/s → t = 2 s, v = +20 m/s → ← t = 6s, v = -20 m/s ← t = 7s, v = -30 m/s t = 1 s, v = +30 m/s → t = 0 s, v = +40 m/s → ← t = 8s, v = -40 m/s a = -10 m/s/s during entire flight

Example A ball is thrown directly up with a speed of 12.0 m/s. How long does it take the ball to reach its maximum height? How long does it take for the ball to land back in your hand? What is its maximum height?

Whiteboard Problem vi = 2.25 m/s d = 25.3 m Mr. Mellon fires a rocket up into the air. It travels directly up and falls back down to its original height. If it was in the air for a total of 4.50 s, determine: A) Initial speed it was launched at. B) Maximum Height vi = 2.25 m/s d = 25.3 m 5

II. Properties of Horizontal Projectile Motion same All objects released from the _______ height will hit the ground at the _______ time, regardless if fired with an initial horizontal velocity same Horizontal and vertical motions are completely _____________ of each other. independent Soccer ball shot from a truck (Mythbusters) (1 min)

II. Properties of Horizontal Projectile Motion Horizontal Motion (X Axis) Vertical Motion (Y Axis) Forces Acceleration Velocity Gravity, acts down None g = - 10 m/s/s acts down None Constant vix = vfx Changing (10 m/s each sec.)

I. Horizontal Projectiles If no gravity 1 s 2 s 3 s -> Parabolic Trajectory (actual path) 4 s -> 5 s -> Vertical Motion Only

I. Horizontal Projectiles

C. Projectile Motion Problem Solving 1. Draw a diagram and identify which directions (x an y) you want to be positive (we always use ________and to the ______________ is positive) up right 2. Create a horizontal (x) and vertical (y) table and break all given values and what you want to find into these components.

C. Projectile Motion Problem Solving 3. Remember general information: A) ay = g = -10 m/s/s - the projectile experiences a constant downward acceleration B) ax = zero - the object does not accelerate in the horizontal component (vi, x = vf, x) C) If fired horizontally, viy = 0 m/s

D. Horizontal Projectile Examples 1. A physics student from Pittsford throws a ball thrown horizontally from the top of a building with a speed of 8 m/s. The student, wishing to test her knowledge, measures the height of the building to be 15 m. A) What is the ball’s acceleration in x and y components? B) What is the ball’s initial vertical (y) velocity? C) How long does it take for the ball to hit the ground? D) How far away did the ball land from the building?

2. A plane drops a package on a friendly village 2. A plane drops a package on a friendly village. The plane is traveling 240m/s. The package took 20 s to hit the ground. (Ball shot from moving cart video (15 s)) A) What was the package’s initial velocity? B) What was the plane’s altitude when it released the package? C) How far away from where the plane originally dropped the friendly package did it land?

Horizontal Projectile Whiteboard Problems 1. You are at a circus and you see a stunt man climb up 20 meters into a cannon. He gets fired horizontally out of the cannon and lands 150 m away. A) How long was stunt man in the air for? B) What was his velocity when he came out of the cannon? 2. An arrow is shot at a target 20 m away. The arrow is shot with a horizontal velocity of 60 m/s. A) How long is the arrow in the air for? B) How far does the arrow drop as it approaches the target? 3. A stone is thrown off a 81.5 m cliff with a horizontal speed of 15 m/s. A) How long is the stone in the air for? B) How far from the base of the cliff does the stone hit the ground? 2 s 75 m/s 0.33 s 0.54 m 4.04 s 60.6 m

III. Properties of Angled Projectile Motion: When a projectile is fired at an angle, its initial velocity is broken into two parts, HORIZONTAL and VERTICAL components.

III. Properties of Angled Projectile Motion:

III. Properties of Angled Projectile Motion: Because there is no FORCE acting on the projectile in the horizontal direction, its horizontal velocity component remains CONSTANT. GRAVITY is the force that acts on the object in the vertical direction. This force causes a change in the object’s VERTICAL VELOCITY.

Path of a Projectile

III. Properties of Angled Projectile Motion: As the projectile reaches in maximum height, the VERTICAL component of the velocity DECREASES. At the maximum height the vertical component of its velocity equals ZERO

Horizontal (x) Motion Vertical(y) Motion Vertical Velocity: changes viy = v sinθ Horizontal Velocity: Remains constant vix = v cosθ Vertical Accel.: Equals g (ay = -9.81 m/s2) Horizontal Accel.: ax = 0 m/s2 Only equation: d = vixt Maximum Height: vy = 0 m/s

IV. Symmetry in Angles for Projectiles: View the animation Mr. Mellon shows to you (Golf Range Gizmo) How does the range of a projectile compare when fired at 30 degrees as opposed to a projectile fired at 60 degrees? What angle gives you the maximum range? Gives you the same range 45 degrees

IV. Symmetry in Angles for Projectiles: Conclusions: Projectiles fired at _____________ gives you maximum ________________ Projectiles fired at ___________________ (add up to 90 degrees) give the _________________ 45 degrees range (horizontal distance) complimentary angles same range

Video Clip and Gizmo Simulation You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. On the other hand, you also know that the dart will not travel in a straight line, but rather in a parabolic path like any other projectile. In order to hit the monkey with the dart, where should you point the gun before shooting? Video Clip and Gizmo Simulation 1 Above 2 Right Above 3 Below

Shooting the Monkey... monkey! At an angle, still aim at the monkey! Dart hits the monkey!