Physics in Law The Minneapolis Police Department has hired you as a consultant in a robbery investigation. A thief allegedly robbed a bank in the IDS.

Physics in Law Physics in Law The Minneapolis Police Department has hired you as a The Minneapolis Police Department has hired you as a

consultant in a robbery investigation. A thief allegedly consultant in a robbery investigation. A thief allegedly robbed a bank in the IDS Crystal Court. To escape the robbed a bank in the IDS Crystal Court. To escape the pursing security guards, the thief took the express pursing security guards, the thief took the express elevator to the roof of the IDS tower. Then, in order to elevator to the roof of the IDS tower. Then, in order to not be caught with the evidence, she allegedly threw the not be caught with the evidence, she allegedly threw the money bag to a waiting accomplice on the roof of money bag to a waiting accomplice on the roof of Dayton's, which is just to the west of the IDS tower (they Dayton's, which is just to the west of the IDS tower (they are separated by the Nicollet Mall). The defense attorney are separated by the Nicollet Mall). The defense attorney contends that in order to reach the roof of Dayton's, the contends that in order to reach the roof of Dayton's, the defendant would have had to throw the money bag with defendant would have had to throw the money bag with a minimum horizontal velocity of 10 meters/second. But a minimum horizontal velocity of 10 meters/second. But in a test, she could throw the bag with a maximum in a test, she could throw the bag with a maximum velocity of no more than 5 meters/second. How will you velocity of no more than 5 meters/second. How will you advise the prosecuting attorney? You determine that the advise the prosecuting attorney? You determine that the IDS tower is 250 meters high, Dayton's is 100 meters IDS tower is 250 meters high, Dayton's is 100 meters high and the Mall is 20 meters wide. high and the Mall is 20 meters wide.

Physics in LawPhysics in Law

IDS tower

mall

Dayton’s

ProjectProject Observe and compare a launched steel Observe and compare a launched steel

ball to a dropped steel ball.ball to a dropped steel ball. Describe and explain your observations.Describe and explain your observations.

Lesson #17Lesson #17Topic: Topic: Independence of Vectors

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Observe and describe simultaneous horizontal Observe and describe simultaneous horizontal and vertical motion.and vertical motion.

2.2. Analyze and explain projectile motion.Analyze and explain projectile motion.

10/13/06

Assignment: “Concept Development 3-1” Due Tuesday!

Warm Up: A hunter is standing upright and fires a shot off at a deer. He fires the rifle completely horizontally. The empty shell is released from the chamber of the gun at the same moment the bullet leaves the barrel. If he misses the deer, does the bullet or empty shell hit the ground first?

Does the bullet or empty shell hit the ground first?

Bulle

t

Shel

l

They

hit

at th

e sa

me

...

They

hit

at s

lightly

dif.

..

0% 0%0%0%

1.1. BulletBullet

2.2. ShellShell

3.3. They hit at the They hit at the same timesame time

4.4. They hit at slightly They hit at slightly different times but different times but I’m not sure which I’m not sure which one hits firstone hits first

0 of 20

Independence of VectorsIndependence of Vectors The X component of a vector will not affect or The X component of a vector will not affect or

change the Y component of that vector.change the Y component of that vector. Example: A ball fired horizontally will hit the Example: A ball fired horizontally will hit the

ground at the same time as a ball dropped from ground at the same time as a ball dropped from rest.rest.

The horizontal velocity does not change the time The horizontal velocity does not change the time it takes for an object to hit the ground.it takes for an object to hit the ground.

The vertical acceleration does not increase or The vertical acceleration does not increase or decrease the horizontal velocity. (vdecrease the horizontal velocity. (vxx = constant) = constant)

Objects can have a constant horizontal velocity Objects can have a constant horizontal velocity and a vertical acceleration happening and a vertical acceleration happening simultaneously.simultaneously.

We call this situation We call this situation projectile motionprojectile motion..

Which of the following is Which of the following is FalseFalse??

The

horizonta

l com

p...

The

verti

cal c

ompo

ne..

The

larg

er th

e ho

rizon

t..

A d

ropped

bal

l and

a ..

.

0% 0%0%0%

1.1. The horizontal component of The horizontal component of a projectile is constanta projectile is constant

2.2. The vertical component of a The vertical component of a projectile is constantly projectile is constantly acceleratingaccelerating

3.3. The larger the horizontal The larger the horizontal velocity, the longer the velocity, the longer the object stays in the airobject stays in the air

4.4. A dropped ball and a ball A dropped ball and a ball thrown horizontally from the thrown horizontally from the same height will hit the same height will hit the ground at the same timeground at the same time

0 of 20

Practice ProblemPractice Problem

A car is driving towards a cliff at a constant A car is driving towards a cliff at a constant speed of 20m/s. If the cliff is 45 m tall, speed of 20m/s. If the cliff is 45 m tall, what is the distance from the bottom of the what is the distance from the bottom of the cliff to the point where the car lands?cliff to the point where the car lands?(Draw a picture to guide your thinking)(Draw a picture to guide your thinking)Givens

x y

ProjectProject Walk at a constant speed and drop a ball Walk at a constant speed and drop a ball

into a ring. into a ring.

p85 Practice problems #1-3p85 Practice problems #1-3

Lesson #18Lesson #18Topic: Lab: Independence of VectorsTopic: Lab: Independence of Vectors

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Analyze the vertical and horizontal motion Analyze the vertical and horizontal motion of the same object.of the same object.

2.2. Calculate where a projectile will land given Calculate where a projectile will land given horizontal velocity and distance it will fall.horizontal velocity and distance it will fall.

10/16/06

Original Task: Get a steel ball to roll off the lab table and into a Bull’s-Eye on the floor on the first try.

ProjectProject Play catch with a partner.Play catch with a partner. Observe the motion of the object and be Observe the motion of the object and be

able to describe…able to describe…1.1. The horizontal component of distanceThe horizontal component of distance2.2. The vertical component of distanceThe vertical component of distance3.3. The horizontal component of velocityThe horizontal component of velocity4.4. The vertical component of velocityThe vertical component of velocity5.5. The horizontal component of The horizontal component of

accelerationacceleration6.6. The vertical component of accelerationThe vertical component of acceleration

Practice ProblemsPractice Problems

After you finish the Concept Development After you finish the Concept Development 3-1:3-1:

Page 164-165 problemsPage 164-165 problems

#41, 43, 51, 52, 53 #41, 43, 51, 52, 53

Complete “Physics in Law”Complete “Physics in Law”

Lesson #19Lesson #19Topic: Describing Projectile Motion Topic: Describing Projectile Motion

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Draw a picture of a projectile and the x and Draw a picture of a projectile and the x and y components of its velocity.y components of its velocity.

2.2. Describe how the velocity components of a Describe how the velocity components of a projectile change during its flight path.projectile change during its flight path.

10/18/06

Assignment: “Tossed Ball” handout due tomorrow

Warm Up: A person wants to shoot a monkey hanging from a tree with a slingshot. Should he aim above the monkey, below the monkey, or at the monkey? What if the monkey leaves go of the branch at the same time he fires the slingshot?

If the monkey drops at the same If the monkey drops at the same time the gun is fired, you should time the gun is fired, you should

aim…aim…

Above

the

monke

y

At t

he m

onkey

Bel

ow th

e m

onke

y

Wai

t till

he

drops

and ..

.

0% 0%0%0%

1.1. Above the Above the monkeymonkey

2.2. At the monkeyAt the monkey

3.3. Below the monkeyBelow the monkey

4.4. Wait till he drops Wait till he drops and then chase and then chase him downhim down

0 of 20

University of Minnesota DemoUniversity of Minnesota Demo

Shoot the monkey!Shoot the monkey!

Velocity of a ProjectileVelocity of a Projectile The resultant velocity of a projectile at any The resultant velocity of a projectile at any

instant is dependent on its horizontal and instant is dependent on its horizontal and vertical components at that moment.vertical components at that moment.

The vertical component is the same as an object The vertical component is the same as an object undergoing vertical acceleration. (a ball tossed undergoing vertical acceleration. (a ball tossed straight up)straight up)

vy=20m/s

How long does the ball stay in the air?

Velocity of a projectile Velocity of a projectile

The horizontal component is the same as an The horizontal component is the same as an object moving horizontally at a constant speed. object moving horizontally at a constant speed. (a ball moving in a straight path forward) (a ball moving in a straight path forward)

v= 5m/s

How far will this ball travel in 4 seconds?

The horizontal component of a The horizontal component of a projectile can be treated as…projectile can be treated as…

An o

bject

movi

ng hor

...

An o

bject

movi

ng hor

...

An o

bject

thro

wn stra

...

0% 0%0%

1.1. An object moving An object moving horizontally at horizontally at constant speedconstant speed

2.2. An object moving An object moving horizontally with an horizontally with an acceleration of acceleration of 10m/s10m/s22

3.3. An object thrown An object thrown straight into the airstraight into the air

0 of 20

The vertical component of a The vertical component of a projectile can be treated as…projectile can be treated as…

An o

bject

movi

ng hor

...

An o

bject

movi

ng hor

...

An o

bject

thro

wn stra

...

0% 0%0%

1.1. An object moving An object moving horizontally at horizontally at constant speedconstant speed

2.2. An object moving An object moving horizontally with an horizontally with an acceleration of acceleration of 10m/s10m/s22

3.3. An object thrown An object thrown straight into the airstraight into the air

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Projectile MotionProjectile Motion

x

xx t

dv

yiyfy gtvv yiyfy gdvv 222

vy

vx

v

v = vx

vy

vx

v

vx is constant throughout the path and we can therefore use the equation:

vy can be treated as an object thrown directly upward into the air and we can therefore use the equations:

221

yyiyy gttvd

Lesson #20Lesson #20Topic: Topic: Projectile Motion

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Calculate the resultant velocity vector of a Calculate the resultant velocity vector of a projectile given vprojectile given vxx and v and vy y components.components.

10/19/06

Assignment: Ch 6 p 164 – 165 #44, 46, 55, 58, 59

Project: What is the height of the tree between the tennis courts and the school?

Example ProblemExample ProblemHow tall is the tree next to the school?

vy

vx

vx

vx

vyvv

Givens

x y

vy= 0m/s

dx

dy

Example ProblemExample ProblemWhat was the initial velocity of the ball?

vy

vx

vx

vx

vyvv

Givens

x y

vy= 0m/s

dx

dy

vy

vx

v=?

Practice ProblemPractice Problem A kicker kicks a football 60m down the A kicker kicks a football 60m down the

field. The ball’s highest point is 35m above field. The ball’s highest point is 35m above the ground. What was the initial velocity of the ground. What was the initial velocity of the ball?the ball?

Practice ProblemPractice Problem A model rocket carries no fuel; it is set in A model rocket carries no fuel; it is set in

motion entirely by its ground level motion entirely by its ground level launcher. 8 seconds after being launched, launcher. 8 seconds after being launched, the rocket lands on the ground 410m from the rocket lands on the ground 410m from the launcher.the launcher.

What is the initial velocity of the rocket?What is the initial velocity of the rocket?

Physics Movie StuntsPhysics Movie Stunts Because of your physics background, you have been Because of your physics background, you have been

hired as a consultant for a new movie about Galileo. In hired as a consultant for a new movie about Galileo. In one scene, he climbs up to the top of a tower and, in one scene, he climbs up to the top of a tower and, in frustration over the people who ridicule his theories, frustration over the people who ridicule his theories, throws a rock at a group of them standing on the ground. throws a rock at a group of them standing on the ground. The rock leaves his hand at 30º from the horizontal. The The rock leaves his hand at 30º from the horizontal. The script calls for the rock to land 15 m from the base of the script calls for the rock to land 15 m from the base of the tower near a group of his detractors. It is important for tower near a group of his detractors. It is important for the script that the rock take precisely 3.0 seconds to hit the script that the rock take precisely 3.0 seconds to hit the ground so that there is time for a good expressive the ground so that there is time for a good expressive close-up. The set coordinator is concerned that the rock close-up. The set coordinator is concerned that the rock will hit the ground with too much speed causing cement will hit the ground with too much speed causing cement chips from the plaza to injure one of the high priced chips from the plaza to injure one of the high priced actors. You are told to calculate that speed. actors. You are told to calculate that speed.

Physics Movie StuntsPhysics Movie Stunts

Lesson #21Lesson #21Topic: Topic: Projectiles and Angles

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Draw and label vectors in a projectile Draw and label vectors in a projectile motion diagram.motion diagram.

2.2. Use angles and trig functions to solve Use angles and trig functions to solve projectile motion problems.projectile motion problems.

10/23/06

Assignment: “Ch 6 p 164 -165 #45, 56, 57, 60Ch 6 p 164 -165 #45, 56, 57, 60” due Tomorrow!

Warm Up: A cannon ball is fired at an angle of 35° above the horizontal with a velocity of 60m/s. What are the initial x and y components of this velocity?

Trig review: What is the opposite side of this Trig review: What is the opposite side of this triangle? What is the adjacent side of this triangle?triangle? What is the adjacent side of this triangle?

8co

s30°

,8si

n30°

8si

n30°

,8co

s30°

8/(s

in30

°),8/

(cos

30°)

(sin

30°)/

8,(c

os30°

)/8

0% 0%0%0%

1.1. 8cos30°,8sin30°8cos30°,8sin30°

2.2. 8sin30°,8cos30°8sin30°,8cos30°

3.3. 8/(sin30°),8/(cos30°)8/(sin30°),8/(cos30°)

4.4. (sin30°)/8,(cos30°)/8(sin30°)/8,(cos30°)/8

8

30°

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A projectile is launched with an initial A projectile is launched with an initial velocity of 28m/s at an angle of 30° above velocity of 28m/s at an angle of 30° above

the horizontal. What is vthe horizontal. What is vxx ? What is v ? What is vyy ? ?

24.

2m/s

, 14m

/s

14m

/s, 2

4.2m

/s

56m

/s, 3

2.3m

/s

32.

3m/s

, 56m

/s

0% 0%0%0%

1.1. 24.2m/s, 14m/s24.2m/s, 14m/s

2.2. 14m/s, 24.2m/s14m/s, 24.2m/s

3.3. 56m/s, 32.3m/s56m/s, 32.3m/s

4.4. 32.3m/s, 56m/s32.3m/s, 56m/s

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A cannon ball is fired at an angle of 35° above the horizontal with a velocity of 60m/s. What

are the initial x and y components of this velocity?

34.

4m/s

,49.

1m/s

49.

1m/s

, 34.

4m/s

104

.6m

/s, 7

3.2m

/s

73.

2m/s

, 104

.6m

/s

0% 0%0%0%

1.1. 34.4m/s,49.1m/s34.4m/s,49.1m/s

2.2. 49.1m/s, 34.4m/s49.1m/s, 34.4m/s

3.3. 104.6m/s, 73.2m/s104.6m/s, 73.2m/s

4.4. 73.2m/s, 104.6m/s73.2m/s, 104.6m/s

0of20

Practice ProblemPractice Problem

A ball is launched into the air at an angle A ball is launched into the air at an angle of 60° above the horizontal. It stays in the of 60° above the horizontal. It stays in the air for 4 seconds. What is the initial air for 4 seconds. What is the initial velocity of the ball?velocity of the ball?

Example ProblemExample Problem Draw a projectile motion diagram and

correctly draw and label all vectors for the following problem:

A cannon is aimed 30° above the horizontal. It is fired at a target 312m away and stays in the air for 6 seconds. What is the initial velocity of the cannonball?

Example ProblemExample Problem

θ=30°

vx

viy

vi

dx= 312m

Givens

x y

θ=30°

viy

vi

vx

AssignmentAssignment

Ch 6 Supplemental ProblemsCh 6 Supplemental Problems #1, 2, 4, 11, 12, 13#1, 2, 4, 11, 12, 13

Assignment #2Assignment #2

Standardize Test Practice p169 #1, 6, 8

Complete Physics Movie Stunts

Lesson #22Lesson #22Topic: Topic: Projectile Motion Exam Review

Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Practice solving physics problemsPractice solving physics problems

2.2. Complete and check Exam 3 ReviewComplete and check Exam 3 Review

3.3. Plan a tutoring time (if needed)Plan a tutoring time (if needed)

4.4. Complete a bonus problem opportunityComplete a bonus problem opportunity

10/26/07

Assignment: “Exam Review” due TuesdayProjectile Motion Exam Tuesday!

Warm Up: A girl is sitting in a wagon pulled by her brother. The wagon is moving at 2m/s. She tosses the ball straight upward and the ball stays in her hand for 1 second. What is the initial velocity of the ball relative to the girl? What is the initial velocity of the ball relative to the ground?

A projectile is launched into the air at some A projectile is launched into the air at some angle above the ground. Its angle above the ground. Its horizontal horizontal

velocity at the velocity at the toptop of its path is of its path is

Zer

o

The

sam

e as

the

initi

a...

The

sam

e as

the

initi

..

Dep

enden

t upon

the.

..

0% 0%

100%

0%

1.1. ZeroZero

2.2. The same as the initial The same as the initial vertical velocityvertical velocity

3.3. The same as the initial The same as the initial horizontal velocityhorizontal velocity

4.4. Dependent upon the Dependent upon the angle in which it was angle in which it was thrownthrown

While on the ground trying to hit a friend in a While on the ground trying to hit a friend in a tree house with a water balloon Joe should tree house with a water balloon Joe should

aimaim

Above

his

frie

nd

At h

is fr

iend

Bel

ow h

is fr

iend

Dep

ends

on the

heig

h...

50%

20%

0%

30%

1.1. Above his friendAbove his friend

2.2. At his friendAt his friend

3.3. Below his friendBelow his friend

4.4. Depends on the Depends on the height of the height of the treehousetreehouse

While on the ground trying to hit a friend jumping While on the ground trying to hit a friend jumping out of a tree house, Joe throws at water balloon out of a tree house, Joe throws at water balloon

just as his friend jumps out of the tree. In order to just as his friend jumps out of the tree. In order to

hit him he should aimhit him he should aim

Above

his

frie

nd

At h

is fr

iend

Bel

ow h

is fr

iend

Dep

ends

on the

heig

h...

30%

0%0%

70%

1.1. Above his friendAbove his friend

2.2. At his friendAt his friend

3.3. Below his friendBelow his friend

4.4. Depends on the Depends on the height of the height of the treehousetreehouse

Gravity has no affect on Gravity has no affect on

Ver

tical

vel

ocity

Horiz

ontal v

eloci

ty

The

amount o

f tim

e ..

Gra

vity

affe

cts

all v

ec...

0% 0%0%

100%1.1. Vertical velocityVertical velocity

2.2. Horizontal velocityHorizontal velocity

3.3. The amount of The amount of time an object time an object stays in the airstays in the air

4.4. Gravity affects all Gravity affects all vectors equallyvectors equally

The initial horizontal velocity of a The initial horizontal velocity of a projectile is 15m/s. The final projectile is 15m/s. The final

horizontal velocity is…horizontal velocity is…

0m

/s

5m

/s

-15m

/s

15m

/s

0%

100%

0%0%

1.1. 0m/s0m/s

2.2. 5m/s5m/s

3.3. -15m/s-15m/s

4.4. 15m/s15m/s

BonusBonus

θ= 37°

vi = 105m/s

dy= 125m

dx= ?

θ = ?v = ?

Find: Horizontal distance traveled (2pts), Velocity the ball has when it strikes the ground (2pts), Angle to the vertical that the ball strikes the ground (2pts).