Turn in your homework (Vector Addition Worksheet). Open your journal to the next blank page and set it up as follows: Page: 11 Date: 10-14-16 Title: Projectile Motion EQ: How are horizontal and vertical motion related? Cornell notes, please! Please be ready IMMEDIATELY! We are on pep rally schedule today.

Before we begin… Today’s handout (Projectile Motion Practice) is due on THURSDAY. Write the due date on your paper so there is no confusion! Notice that the answers are already given to you…so what do you think I’m going to be grading???

Motion In Two Dimensions can be considered constant. Projectile Motion Motion In Two Dimensions We restrict ourselves to objects thrown near the Earth’s surface so that gravity can be considered constant.

PROJECTILE MOTION: the motion of an object that is thrown or projected into the air This motion is determined only by the object’s initial velocity (horizontal) and gravity (vertical).

Projectile motion applies to sports.

Projectile motion applies to destructive projectiles.

Projectile motion is a combination of horizontal and vertical vectors.   The horizontal motion of a projectile is constant (because no gravitational force acts horizontally)

The vertical motion of a projectile is just free fall - a constant downward acceleration due to gravity.

A projectile moves horizontally with constant velocity while also being accelerated vertically. The result is a motion in a curved path.

The path of a projectile is its trajectory.   The trajectory of a projectile in free fall is shaped like a parabola.

An object projected horizontally will reach the ground in the same time as an object dropped vertically. No matter how large the horizontal velocity is, the downward pull of gravity is always the same.

The cannonball falls vertically the same amount of distance in each unit of time as it did when it was merely dropped from rest.

Horizontally launched projectile Horizontal velocity is constant. Vertical velocity is changing due to gravitational acceleration.

Important Concepts for Projectiles Launched Horizontally Horizontal Components Vertical Components Horizontal velocity is constant throughout the flight Horizontal acceleration is 0 Initial vertical velocity is 0 but increases throughout the flight Vertical acceleration is constant: -10 m/s2

What equations will I need to use? HORIZONTAL (x) VERTICAL (y) dy = ½ at2 t = 2dy a vy = at dx = vxt

HOMEWORK = #1 A ball is kicked horizontally at 8.0 m/s from a cliff 80m high. How far from the base of the cliff will the stone/ball strike the ground?

What do we know and what are we looking for? vx = 8.0 m/s dy = -80 m (because it’s going down) a = -10 m/s2 vx = 8.0 m/s What are we looking for?? 80 m dx = ?

How do we find dx? Equation for horizontal motion: We have vx…so we need t. How do we figure out how long it takes to hit the ground? Use the vertical motion equations!

Vertical Motion dy = -80 m a = -10 m/s2 What equation should we use? Rearrange the equation to solve for t then plug in values. 𝑡= 2𝑑𝑦 𝑎 = 2(−80 𝑚) −10 𝑚/𝑠2 = −160 𝑚 −10 𝑚/𝑠2 = 16 𝑠2 = 4 s

𝑑𝑥= 8.0 𝑚 𝑠 4 𝑠 =32 𝑚 Horizontal equation Now plug in your vx and t: 𝑑𝑥= 8.0 𝑚 𝑠 4 𝑠 =32 𝑚 So the object hits 32 m away from the base of the cliff. Could you figure out the resultant displacement if I asked??

Resultant Displacement Use a2 + b2 = c2 ! dy = -80 m dx = 32 m dR = 86 m dR (-80 m) 2 + (32 m)2 = dR2 6400 m2 + 1024 m2 = dR2 7424 m2 = dR2 7424 m2 = dR

Cliff example A boulder rolls off of a cliff and lands 6.39 seconds later 68 m from the base of the cliff. What is the height of the cliff? What is the initial velocity of the boulder? What is the velocity of the boulder just as it strikes the ground?

How high is the cliff? dy= ? a=-10 m/s2 t = 6.39 s vx=? Vy = 0 dx= 68 m The cliff is 200 m high

What is the initial velocity of the boulder? The boulder rolls off the cliff horizontally Therefore, we are looking for Vx