Dropped object Lab Displacement vs Time for accelerated motion

What are the velocities for a rock dropped from rest? 0 m/s 1s -10 m/s What are the velocities for a rock dropped from rest? 2s -20 m/s 3s -30 m/s -40 m/s 4s

What is the Total Displacement at each second 0 m/s -45 m -20 m -80 m -5 m 1s 10 m/s What is the Total Displacement at each second 2s 20 m/s 3s 30 m/s 4s 40 m/s

Displacement changes with t2

Dy v = Dt Dv (v2 + v1) a = v = Dt 2 Derivation of Displacement = constant * t2 Dy v = Dt Dv a = Dt (v2 + v1) 2 v =

at2 Dy = v1t + 2 Time elapsed (s) displacement (m) acceleration m/s2 2 Time elapsed (s) Initial velocity m/s displacement (m)

at2 Dy = v1t + 2 If you start from rest Dy = at2 2

If the acceleration is due to gravity. 9.8 m/s2 Dy = at2 2 Dy = 4.9 t2

Distance fallen by an object in freefall dropped from rest g Dy = at2 2 time falling How far you fall THIS ONLY WORKS if the object was dropped from rest

Dy = gt2 2

How far has a rock dropped 3 seconds after release? 0 m/s 1s -5 m -20 m -45 m -80 m 10 m/s How far has a rock dropped 3 seconds after release? 2s 20 m/s 3s 30 m/s Dy = gt2 2 4s 40 m/s

How far has a rock dropped 3.5 seconds after release? 0 m/s 1s -5 m -20 m -45 m -80 m 10 m/s How far has a rock dropped 3.5 seconds after release? 2s 20 m/s 3s 30 m/s Dy = at2 2 4s 40 m/s

A rock is dropped from rest and hits the ground 5 seconds later A rock is dropped from rest and hits the ground 5 seconds later. How high was it when it was dropped?

How long will it take a rock which is dropped from rest to fall 320 m?

A person jumps up and hits the ground 1. 2 seconds later A person jumps up and hits the ground 1.2 seconds later. How high did they go?

Quick review. A rock has the velocity vector below 1 dm = 5 m/s V How fast is it moving horizontally & vertically?

Section 3-4 A projectile is a moving object only influenced by gravity PROJECTILE MOTION

A ball rolls across a table at a constant speed Finish the motion diagram

A ball rolls across a table at a constant speed Finish the motion diagram

Equal Spacing for Constant Horizontal Speed

Let’s put velocity vectors on the balls at different each frame Let’s put velocity vectors on the balls at different each frame. The first one is done Is the ball accelerating?

Finish the motion diagram for a dropped ball

Finish the motion diagram for a dropped ball

Is the ball accelerating? In what direction is it accelerating? What happens to it horizontal speed As gravity pulls on it?

Lets place velocity vectors on the ball as time passes, the first one is done.

What would a motion diagram look like if a ball Had a constant horizontal speed, but got faster and faster traveling down?

Constant Horizontal Speed Increasing downward speed

Constant Horizontal Speed Increasing downward speed

What is the shape of the path?

What is the shape of the path? A Parabola

What happens to the VERTICAL distance fallen each second? WHY?

What happens to the HORIZONTAL distance traveled each second? WHY? It’s Horizontal Velocity (Vx) is CONSTANT, because Gravity only accelerates it in the Y direction

The horizontal movement is the same each time The vertical movement increases each time

A rock is dropped from rest. What is its speed after 1 second 2 seconds etc..

Cannonball is launched horizontally with a VX = +20 m/s After 1 second what is its X velocity? 4 s

0 s 20 m/s 1 s 20 m/s 0 m/s 2 s 20 m/s 3 s 20 m/s If the cannon is shot perfectly horizontally, how fast is it traveling down immediately after exiting the cannon? 4 s

After 2 seconds of falling? 10 m/s 2 s 20 m/s 3 s 30 m/s How fast is it moving vertically After 1 second of falling? 4 s After 2 seconds of falling? 40 m/s

(one DOES NOT affect the other) 20 m/s 1 s 20 m/s 10 m/s 2 s 20 m/s 20 m/s 3 s 20 m/s 30 m/s Horizontal Speed & Vertical Speed Are INDEPENDENT (one DOES NOT affect the other) 4 s 20 m/s 40 m/s

Gravity ONLY affects the VERTICAL SPEED. 20 m/s 1 s 20 m/s 10 m/s 2 s 20 m/s 20 m/s 3 s 20 m/s 30 m/s Gravity ONLY affects the VERTICAL SPEED. The horizontal speed is unchanged 4 s 20 m/s 40 m/s

What are the RED arrows shown? 20 m/s 1 s 20 m/s 10 m/s 2 s 20 m/s 20 m/s 3 s 20 m/s 30 m/s What are the RED arrows shown? The sum of its Vx and Vy. Which is..? 4 s 20 m/s The actual speed and velocity of the cannonball at that instant. 40 m/s

0 s 20 m/s 1 s 20 m/s 10 m/s 2 s 20 m/s 20 m/s 3 s 20 m/s 30 m/s The instantaneous velocity is the resultant of its horizontal and vertical velocities 4 s 20 m/s 40 m/s

WHY?? VX is constant Vy increasing (negative) What happens to the speed and direction of the cannonball? 1 s 2 s 3 s WHY?? VX is constant Vy increasing (negative) 4 s

Two marbles are dropped from the same height above the floor Two marbles are dropped from the same height above the floor. Which hits the floor first???? The red one is rolled off The blue one is just dropped

DEMO- which hits the ground first?

They both hit at the same time!!

They both start with a vertical velocity of 0. (Vy =0) The horizontal velocity (Vx) doesn’t affect how fast it falls, but is does affect…… How far away it lands

A bullet is fired horizontally at 120 m/s. After 2 seconds, what are is horizontal and vertical velocities? What is it’s resultant velocity, magnitude only?

A cannonball is fired horizontally at 64 m/s. After 4.2 second, how far has traveled horizontally and vertically? What happens to the resultant velocity of the cannon ball as it falls?

A rock is thrown with horizontal velocity shown below A rock is thrown with horizontal velocity shown below. What is its vertical velocity after 2.5 seconds? It resultant velocity? 1 dm = 10 m/s

WS 3-4

Dy = at2 2 A marble is dropped off a table 1.0 m high. How long does it take to hit the ground? Dy = at2 2 1.0 m

If the marble was rolling off the table at 2. 0 m/s horizontally If the marble was rolling off the table at 2.0 m/s horizontally. How long does it take to hit the ground and how far does it travel horizontally? 1.0 m

A rifle is fired horizontally A rifle is fired horizontally. At the same time a stone is dropped from the same height. Which hits first? Which is traveling faster when it hits?

A car is driving at 15 m/s (horizontally) when it runs off a bridge which is 25 meters above the ground. How far horizontally does the car go before it crashes? What is the cars resultant velocity just before it crashes? V = Vx + Vy

A car lands 23 meters away from the base of a bridge which is 12 meters high. How fast was it driving?

A girl has a water balloon and a slingshot on a hill. She wants to splash a boy who is hanging from tree at the same height. If the balloon is shot at the same time the boy drops from the tree, should she aim higher, lower, or right at the boy?

How far has the balloon fallen vertically? She throws the ball straight, after 1 second the ball has traveled a distance to the right (X). How far has the balloon fallen vertically? How far has the boy fallen? X 5 m 5

After 2 seconds how far did the balloon go horizontally? How far has the balloon fallen? How far has the boy fallen? X X 5 m 20 m 20 m

After 3 seconds how far did the balloon go horizontally? How far has the balloon fallen? How far has the boy fallen? X X X 5 m 20 m 45 m

They both fall at the same rate so they are both at the same height? At any given time.

What if she had thrown the ball harder, Would the balloon still have hit the boy? Old path

After one second of travel what would be different if it were thrown faster horizontally? X

Where will it be after 2 seconds? X X SPLAT

What would the path be if the balloon had been thrown slower?

What doesn’t change? How far they have fallen (down) As time passes.

How far they have fallen (down) at any moment in time What doesn’t change? How far they have fallen (down) at any moment in time 5m 20 m 45 m

Do the balloon & the boy have the same speed when they hit the ground?

They have the say vertical speed (Vy) 10 m/s 10 m/s 20 m/s 20 m/s 30 m/s

But the balloon also has a horizontal velocity (Vx). So its resultant (total) velocity is greater. 10 m/s 10 m/s 20 m/s 20 m/s 30 m/s

at2 Dy = 2 If there was no gravity. It would follow a straight line path. 5 m 20 m 45 m With no initial Vertical speed (and down as negative) How far it fell DOWN = 80 m at2 Dy = 2 125 m

What would the path of a projectile look like if it were thrown at an angle down?

If there was no gravity It would follow a straight line path.

With Gravity it will fall an extra at2 5 m Dy = 2 20 m 45 m 80 m

What if it were thrown up with no gravity

45 m 20 m 80 m 5 m 125 m

A rock is shot at an angle will follow a parabolic path

By forming a parallelogram we can find, the INITIAL horizontal and vertical velocities VY VX

Plugging in numbers for velocities VY VY = 20 m/s VX = 20 m/s

What will happen to it horizontal speed as it travels.? 20 m/s

If the projectiles was in the air for 4 seconds, how far away does it land? 20 m/s

What will happen to it VERTICAL Velocity as it travels? The pictures are at 1 second intervals none 10 m/s 20 m/s -10 m/s -20 m/s

How long was it in the air? How long did it take to reach the highest point? (Tup) How long did it take to fall back down from the highest point? (Tdown) none 10 m/s 20 m/s -10 m/s -20 m/s

How high did it go? none 10 m/s 20 m/s -10 m/s -20 m/s

Compare the initial vertical speed to the vertical speed when it hits the ground none 10 m/s 20 m/s -10 m/s -20 m/s

What will happen to its Resultant Velocity as it travels? Compare the resultant speed when it hits the ground to the speed at which it was fired

Is the velocity zero at the top?

An object is shot upward at 40 m/s vertically & 50 m/s horizontally Find Tup Ymax Tair DX 40 m/s 50 m/s

8 s 320 m 4 s up 40 m/s 80 m 40 m/s How long is it in the air? How far does it go horizontally? 4 s up 40 m/s 80 m 40 m/s

vy = vy = Find the initial horizontal and vertical velocities Dv Find tup a = t Find average velocity on the way up vy = v1 + v2 2 Find max height vy = Dy t

vx = How to solve trajectory problems Find tair tair = 2 tup Find horizontal distance vx = Dx t Dx = vx tair

A projectile is fired at 65 m/s at an angle of 35o Find Initial X & Y velocity Find Tup Find Ymax Find Tair Find DX

402 + 402 = R2 R = 56 m/s Our first example the object was shot at 45o What was the resultant velocity at which it was shot? 402 + 402 = R2 40 m/s 40 m/s R = 56 m/s

WS 3-6

What happens to the component velocities as the angle gets flatter?

How will its path be affected if shot at the same speed but a steeper or shallower angles? 40 m/s 40 m/s

How will its path be affected if shot at the same speed but a steeper or shallower angles? 40 m/s 40 m/s Which velocity affects how long the projectile is in the air? Which velocity affects how high it goes?

How does the angle of release affect ymax? 45 90o 75o 60o 45o 30o 15o

Which will be in the air the longest? 45 o 30o 15o

90o How does the angle of release affect Dx? 75o 60o 45o 45 o 30o 15o

What do you notice about the paths with the same colors? 75 o 60 o 45o 45 o 30 o 15 o

A rock is launched at 75 m/s at an angle of 22o? Find tup, max height, tair, horizontal distance? What is the objects resultant velocity at it’s peak? What is the objects resultant velocity when it hits?

A dart is launched from level ground, it is in the air for 2 A dart is launched from level ground, it is in the air for 2.6 seconds and lands 25 m away from where it was launched. What was the initial vertical and horizontal speed of the dart when it was launched? What was the speed and angle of its launch velocity?

We have been calculating the IDEAL Path of a projectile. What have we been neglecting? Air resistance!! 45o 45 o

Air resistance will slow its vertical speed So it won’t go as_______ HIGH And its horizontal speed So it won’t go as_______ FAR 45o 45 o Actual path

Satellites Does the earth’s gravity affect them?

Why doesn’t an object which orbits the earth fall to the ground?

Satellites follow circular orbits around the earth What keeps them from flying into outer space?

Consider this a ball is thrown horizontally at 8 m/s From a height of 5 m. How long does it take to hit the ground? How far away does it land? 1 s 8 m 8 m 5 m

What if it is thrown twice as fast at 16 m/s? How long does it take to hit the ground? How far away does it land? 1 s 16 m (twice as far) ASSUMING THAT THE GROUND IS LEVEL 5 m

BUT…. Earth’s surface only looks flat Because…..

The earth’s surface actually curves down about 5 m every 8,000 m (or about 3 feet every mile) Picture is not to scale!!! 8,000 m 5 m

If a cannon ball is shot at 8,000 m/s horizontally, How far will it travel horizontally in 1 second? How far will it fall in 1 second. 8,000 m 5 m

How high is it above the ground? The same as when it started!! The cannon ball is now in orbit!! 8,000 m 5 m

If a cannon ball is shot at 8,000 m/s horizontally, How far will it fall in 1 second. How far will it travel horizontally in 1 second? 8,000 m 5 m

Shooting cannon balls If a cannonball is shot relatively slowly gravity pulls it down quickly to the surface

gravity free path Shooting cannon balls If a cannonball is shot relatively slowly gravity pulls it down quickly to the surface

More here showing gravity free path vs with gravity etc.. for next year.

Shooting cannon balls Shooting cannon balls If a cannonball is shot a bit faster it goes further but is still brought down

Shooting cannon balls Shooting cannon balls If a cannonball is shot much faster it escapes the planets gravity

Shooting cannon balls Shooting cannon balls it continues to fall, but it tangential velocity keeps it from ever hitting the planet. It is in orbit. Somewhere in between the last 2 shots

Shooting cannon balls Shooting cannon balls THE CANNON BALL IS IN ORBIT

An object shot a 8,000 m/s will orbit the earth’s surface. A high speed rifle bullet travels only about 750 m/s. If a cannonball could be launched at that speed, why would it realistically crash into the ground? AIR RESISTANCE At this speed friction with the air would slow it down (and probably melt it like a shooting star)

Find the initial horizontal and vertical velocities tup = vy1 g Find tup a = t Find average velocity on the way up vy = v1 + v2 2 vy = vy1 2 Find max height vy = Dy t Dy = vy tup