Unit 3: Projectile & 2D Motion http://www.youtube.com/watch?v=sFcsMDzW1Yg

Projectiles Airborne objects that move as a result of their own inertia and gravity. They exhibit two dimensional motion. Horizontal and vertical motion Horizontal and vertical motion are independent of one another. The resultant motion is a combination of horizontal and vertical motion.

2 Dimensional Motion Projectiles Riverboats & Airplanes Gravity affects outcome Riverboats & Airplanes Gravity does not affect outcome

If a cannonball is projected horizontally from the top of a cliff If a cannonball is projected horizontally from the top of a cliff. In the absence of gravity, the cannonball would continue its horizontal motion at a constant velocity. Horizontal velocity is constant (ax = 0) If dropped from rest in the presence of gravity, the cannonball would accelerate downward. Vertical velocity gains speed (ay = -9.8 m/s2)

Monkey In the Absence of Gravity

Why Does the Hunter Miss the Monkey

The Hunter Now Aims

Strategies for Applying Kinematic Equations in 2 Dimensions Make a drawing of the situation. Decide which directions to be called positive and negative. Do this for both the x and y directions. Remember that the time variable is the same for both x and y. Make note of all the assumed information. Starts at rest. Stops When motion is divided into two segments, remember the final velocity for one segment becomes the initial velocity for the next segment.

Two Types of Projectiles

Steps to working a problem Draw the picture Label with variables and numbers Write the givens Write what you are looking for Write equation Plug and chug Answer with number and unit!

Anytime the object starts at a given height Do not multiply time by 2….since starts at max height already

Anytime an object starts at an angle from the ground! Vy at the highest peak is always 0 Remember when use max height and Vy=0….it’s only half the time the object stays in the air So…to find total distance (dx)…multiply time by 2

EX 1: A football is kicked at an angle of 45º to the ground with a speed of 25 m/s. You will be able to Calculate … A. The initial horizontal velocity B. The initial vertical velocity C. Maximum height reached

EX 2: A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate … … note – think of various ways this question could be formed on a test (cannon fires, football thrown, baseball hit, golf ball hit, soccer ball kicked, etc.) A. Maximum height of projectile B. Launch Velocity C. Launch angle

A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate … A. Maximum height of projectile. Answer … -Begin with equation -Use the fact that at top of trajectory Vyi is zero. -Use second half of trajectory. -Plugging in values:

A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate … B. Launch Velocity. Answer … Need X and Y velocities (Vx and Vy). Vx is found using: Vy is found using half of trajectory and: Knowing that Vy is zero at half the time … So …

A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate … C. Launch Angle. Answer … Use triangle and trig function. So θ

Ex 3:An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate … … note – think of various ways this question could be applied (dropped from a moving vehicle, dropped by a flying object, rolls off a cliff, rolls off a table, etc.) A. Velocity of object

An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate … A. Velocity of object. Answer: Typical to these types of problems, first step would be to find the time in the air (fall time). This is found using the vertical distance (dy).

An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate … Velocity of object. Answer: Then use time (8.45 s) with X distance (dx) to calculate horizontal velocity (Vx).

Ex 4: An object is travelling at 37◦ with an initial velocity 8 m/s Ex 4: An object is travelling at 37◦ with an initial velocity 8 m/s. How long will it take to go 38 m horizontally? … note – think of various ways this question could be applied (boat/swimmer crossing river, airplane, ball thrown from vehicle, etc..)

An object is travelling at 37◦ from vertical at velocity 8 m/s An object is travelling at 37◦ from vertical at velocity 8 m/s. How long will it take to go 38 m horizontally? Need X component velocity. Answer: Note that (similar to projectiles) time is shared between two motions. Each component is independent of the other. θ=37

Review Questions In the absence of gravitational force and friction, describe the motion of an object. How do you describe horizontal motion? Is vertical motion influenced by gravitational force? How far is an object being thrown horizontally given an initial speed of 20 m/s from a 45 m tower?