ABRHS P Chapter 2.5-2.9: Linear Motion...

ABRHS PHYSICS (CP) NAME: ____________________ Chapter 2.5-2.9: Linear Motion 2

2015-16

Text: Chapter 2.5-2.9 Think and Explain: 4-8 Think and Solve: 2-4 Vocabulary: constant acceleration, acceleration due to gravity, free fall Equations:

s = dt

v = Δxt

2

if vvv

+= 2

21 attvd i += atvv if += vf

2 = vi2 + 2aΔx

Constants: g = ±10 m/s2 Key Objectives: Concepts Distinguish between constant speed, constant velocity and constant acceleration. Understand when to use constant acceleration equations. Describe what happens to the velocity of an object in free fall. Describe how far and object in free fall falls every second. Explain how the velocity of a tossed ball changes every second. State the velocity and acceleration of a tossed ball at the top of its path. Sketch the position vs. time, velocity vs. time and acceleration vs. time graphs for an object in

free fall. Sketch the position vs. time, velocity vs. time and acceleration vs. time graphs for an object

tossed into the air. Problem Solving Solve constant acceleration problems using the equations above. Solve free fall problems using the equations above and substituting g for a. Solve ball toss problems using the equations above and substituting g for a.

CP Physics 11-12 Linear Motion II Date Class Reading Homework What is constant

acceleration? Start Constant Acceleration Problems

Finish Constant Acceleration Problems

Constant Acceleration Equations & Examples

More Constant Acceleration Problems

Lab 2-6: Free Fall Finish Lab Free Fall-How fast? How

far? Graphs of Free Fall Reaction Time

2-5, 2-6, 2-8, 2-9

Free Fall Concept WS

Free Fall Problems RQ 15-21, PC 6-8 Movie: How Tall is Niagara

Falls?

Lab 2-7: Up and Down Lab Finish Lab Ball Toss Notes RQ 18, Ball Toss

Concept Sheet Ball Toss Problems Finish Ball Toss

Problems Lab 2-8: The Acceleration of

a Bouncing Ball Finish Lab

Review for Super Quiz Study for Quiz Super Quiz

Constant acceleration Free fall Ball toss

ABRHS PHYSICS (CP) NAME: ___________________

Constant Acceleration Problems

side 1

1. A car on the highway constantly accelerates from an initial speed of 20 m/s to a final speed of 30 m/s over a time of 5 seconds. a. What was the car's acceleration? b. What was the car's average speed? c. How far did the car travel during this 5 seconds?

2. A Boeing 767 airplane can accelerate at a rate of 3.3 m/s2. If a 767 starts from rest,

a. How many seconds will it take to reach a take-off speed of 100 m/s? b. What would be the average speed of the plane over this interval? c. How far would it travel in that time?

3. Bill constantly accelerates from rest, covering a distance of 20 meters in a time of 3.0 seconds.

a. What was his final velocity? (Hint: find the average speed first.) b. What was Bill's acceleration?

4. Emily is riding her bike with a speed of 5 m/s. She then constantly accelerates at a rate of 2 m/s2

until she reaches a speed of 10 m/s. a. How long will it take her to reach a speed of 10 m/s? b. What is her average speed for this interval? c. How far will she travel in that time?

5. Chelsea is rollerblading down Charter Road with a velocity of 18 m/s when a small child jumps out

in front of her, and she attempts to stop. If her acceleration was a constant rate of -1.5 m/s2, a. After 4 seconds, how fast is Chelsea going? b. How many total seconds will it take her to stop? c. How far does she travel before she comes to rest? d. Why is her acceleration negative?


Constant Acceleration Problems

side 2

6. John is on a skateboard in the gym. His initial velocity is zero. Ernie comes along and pushes John with a constant acceleration across the gym floor. John travels a distance of 20 m in 8 s. a. What is John’s average velocity? b. What is John’s final velocity after the 8 seconds? c. What is John’s acceleration across the gym floor?

7. You’re driving your car across a flat parking lot. You’re traveling at 20 m/s when you shift into

neutral and coast to a stop. You’re experiencing a constant acceleration due to the force of friction and air resistance. You stop 8.0 seconds after shifting into neutral.

a. What is the average velocity of the car? b. What is the acceleration of the car? c. Why is the acceleration negative? d. How far did the car coast? 8. Jocko the clown is on a sled initially at rest at the top of the hill. Due to the pull of gravity, he

comes down the hill with constant acceleration. At the bottom of the hill he reaches a maximum speed. Then, he coasts to a stop after traveling 40 m across the flats in 8.0 seconds. a. Draw a picture of the situation. Show where the speed is 0, where the maximum speed is, and where the 40 m and 8 seconds are.

b. What is his average velocity across the flats?

c. What is his velocity at the bottom of the hill? (This is the same as the initial velocity across the flats.)

d. If it takes Jocko 4.0 s to accelerate down the hill, what is his acceleration down the hill? Answers: 1. a) 2 m/s2 b) 25 m/s c) 125 m 2. a) 30.3 s b.) 50 m/s c) 1515 m 3. a) 13.2 m/s b) 4.4 m/s2 4. a) 2.5 s b) 7.5 m/s c) 18.75 m 5. a) 12 m/s b) 12 s c) 108 m 6. a) 2.5 m/s b) 5.0 m/s c) 0.63 m/s2 7. a) 10 m/s b) –2.5 m/s2 d) 80 m 8. b) 5 m/s c) 10 m/s d) 2.5 m/s2

ABRHS PHYSICS (CP) NAME: ____________________ More Constant Acceleration Problems

1. A happy physics student is leaving school for the day. This student uniformly accelerates her car from rest with an acceleration of 1.2 m/s2. a. How long does it take her to reach 15 m/s?

b. How far does she travel in this time? 2. A car is uniformly accelerated at the rate of 2.5 m/s2 for 12 s.

a. If the original speed of the car is 8 m/s, what is its final speed?

b. How far does the car travel in this time? 3. A race car decreases speed uniformly from 55 m/s to 44 m/s in 11 seconds.

a. What is the acceleration of the car?

b. How far does the car travel during this time? 4. Mary is riding her bike with a speed of 14 m/s, when she constantly decelerates and comes to rest

in 7 seconds. a. What is Mary’s acceleration?

b. How far does Mary travel while decelerating? 5. A ball rolling down an incline for 0.75 s undergoes a uniform acceleration of 4.2 m/s2. The ball

has an initial speed of 2.2 m/s when it starts down the incline. a. How long is the incline?

b. How fast is the ball moving at the bottom of the incline? 6. A car traveling west at 44 m/s is uniformly decelerated to a speed of 22 m/s over an 11 second

period. What distance does the car travel over this time? Answers: 1. a. 12.5 s b. 93.8 m 2. a. 38 m/s b. 276 m 3. a. – 1 m/s2 b. 545 m 4. a. -2 m/s2 b. 49 m 5. a. 2..83 m b. 5.35 m/s 6. 363 m


Lab 2-6: Free Fall

side 1

Purpose: 1. To make and interpret the motion graphs for a freely falling ball using the Motion Detectors.

2. To determine if an object falls with constant velocity or constant acceleration. 3. To determine how the placement of the motion detector affects the acceleration. Diagram:

L a bPro

computer motion detector

ball

Procedure: 1. Set up the motion detector on a stand as shown. Make sure that the detector is pointing to the

ground and at least several inches over the edge of the lab table. 2. Start Logger Pro and open up the file "02 Ball." 3. Hold the ball several inches below the motion detector. 4. Start timing. When you hear the detector clicking (a couple seconds after clicking on the green

“collect” button.), let go of the ball. Be careful to not give the ball any initial velocity, and be careful to get your hands out of the way of the detector.

5. The resulting graphs will be pretty messy because they will show a lot more than just the ball falling. Ignoring all the extra clutter of the graphs, sketch the shape of the graphs while the ball was falling in the data section below. Label the axes as well.

6. Make an appropriate best fit line for the velocity graph for the portion of the graph that shows the ball falling. Record the slope, including units, next to the graph.

7. Repeat the above, except this time place the motion detector on the floor. Hold the ball chest high over the detector, start recording, drop the ball, and catch it before it lands on the detector. (Your teacher may have a screen to place over the motion detector as an added safety – if not, place some books around it so that the ball cannot actually land on the detector.)

Data: Motion Detector Looking Down:

slope = _________

Motion Detector Looking Up:

slope = _________


Lab 2-6: Free Fall

side 2

Conclusion: 1. While it was falling, was the velocity of the ball constant? Explain. 2. While it was falling, was the acceleration of the ball constant? Explain. 3. What were the equations that give the velocity as a function of time for both trials? (Remember

to use “v” and “t” instead of “y” and “x” and remember the units.) a. Motion Detector Looking Down: b. Motion Detector Looking Up:

4. a. What was true about the magnitudes of the accelerations you found? What does that mean? b. What about the signs of the accelerations? What does that mean? 5. What was the class average for the acceleration due to gravity? 6. The class probably found that the acceleration was less than 9.8 m/s2. Why do you think that

happened? 7. Why do we tend to round the acceleration due to gravity to be 10 m/s2? 8. In what direction does gravity ALWAYS point? Follow Up Questions: Use g = 10 m/s2 for the following problems. 7. When you drop something on the earth, how much faster does it move for every second that it

falls? 8. If you drop a rock, how fast is it going after 5 seconds? 9. If you drop a rock, how fast is it going after 3.2 seconds? 10. If a falling rock has a speed of 15 m/s, what is its speed 1 second later? 11. If a falling rock has a speed of 5 m/s, what is its speed 1.5 seconds later?

ABRHS PHYSICS (CP) NAME: ________________

Free Fall Concept Sheet

On the surface of the earth, the acceleration due to gravity is about 10 m/s2. Ignoring air resistance, this means that all objects speed up (or slow down) at a constant rate of 10 m/s/s. On this sheet, you will calculate and draw the position of a falling object.

1. Calculate the speed of a falling object for each second of its fall for the first 6 seconds of its fall. Record your answers in the column marked “Speed.” (Show your work below the chart.)

2. Calculate the total distance the object would have fallen for each second of its fall. Record the answers in the “Distance Fallen” column of the chart below. (Show your work below the chart.)

3. For each of the calculated values, place a circle next to the appropriate mark in the diagram. Label it with the appropriate time and speed. (The initial position is already done.)

4. Draw in arrows that could represent the velocity of the ball at each moment.

Time (s)

Speed (m/s)

Distance Fallen

(m) 0 0 0

1

2

3

4

5

6

180

t = 0 v=0 m/s

20

40

60

80

120

140

160

100

ABRHS PHYSICS (CP) NAME: __________________

Free Fall Problems

Answers: 1. a) 40 m/s b) 80 m 2. a) 23 m/s b) 26.5 m 3. a) 12.5 m/s b) 7.8 m 4. a) 0.63 s b) 6.3 m/s 5. a) 1.6 s b) 16 m/s 6. a) 22 m/s b) 21.8 m

1. You are standing on the edge of a cliff by the sea and drop a rock. It falls for 4 seconds, and splashes into the water. a. What is the speed of the rock just as it hits the water? b. How high was the cliff?

2. A worker on the edge of a building drops a hammer. It falls for 2.3 seconds before hitting the ground. a. How fast is the hammer going just as it hits the ground?

b. How tall was the building?

3. A seagull drops a clam onto some rocks in order to crack the shell. The clam falls for 1.25 seconds. a. How fast is the clam going just as it hits the ground? b. How high up was the seagull?

4. A ball is dropped and falls for 2 meters before hitting the ground. a. How many seconds did it take to fall? b. How fast is the ball going just as it hits the ground?

5. A painter drops a paintbrush while painting the side of a building. The brush falls 12..8 meters.

a. How many seconds does it take to fall? b. How fast is the brush going just as it hits the ground?

6. Someone throws a rock straight down with an initial speed of 7 m/s. It falls for 1.5 seconds.

a. How fast is it going when it hits the ground? b. How far did the rock travel?


Movie Analysis: How Tall are Niagara Falls?

Purpose: To analyze the physics of a scene from the movie Superman II. Procedure:

1. Watch the movie clip once to familiarize yourself with all the action. 2. Watch it a second time, but this time use a stop watch to record the time the little boy falls.

Data:

Time Little Boy Falls: __________ seconds Calculations: 1. If the boy had fallen for the amount of time shown in the movie: How far would he have fallen? 2. How fast would the little boy be moving when Superman catches him? 3. When Superman finally catches the boy, it only takes a fraction of a second to stop the boy from

falling. Let’s call it 0.5 seconds to stop the little boy. a. What would be the acceleration of the boy during the catch? b. How many times greater than the acceleration due to gravity is this acceleration? c. How “happy” would the little boy (and his mother) be if that really happened?

4. In reality, Niagara Falls is only 53.6 meters high.

a. How many seconds would it take to fall that distance? b. How fast would an object be going at the bottom?

5. In reality, people’s acceleration while they fall isn’t a constant 10 m/s2. (Why?) After about 30

seconds, people will have reached what is called terminal speed – and then fall with a constant speed. a. If the little boy had fallen 53.6 meters in the time you measured, what would be his average

speed? b. How does this compare to a person’s terminal speed of about 50 m/s?

ABRHS PHYSICS (CP) NAME: _______________

Lab 2-7: Up and Down

side 1

Purpose: 1. To make and interpret motion graphs for the following situations: a. A ball tossed up in the air. b. A cart given an initial push up a ramp. 2. To show that an object can have zero velocity, yet be constantly accelerating. Procedure: Part I: Tossing a ball in the air

1. Place the Motion Detector in on a stool pointing straight up. 2. Start Logger Pro and open up the file "06 Ball Toss." 3. Hold the ball directly above the Motion Detector. 4. Start timing. After you hear the Motion Detector clicking, toss the ball straight up in the air

a few times. Obviously, make sure you catch it and don’t let it crash into the Motion Detector. The goal is to get the ball to record the ball going up and down. (Try a few times in a row – this may be difficult. Call your teacher if you are not having any luck.)

5. Make sure your graph shows the ball going up and down. There will definitely be some “weirdness” in the graphs on either side of this motion and we will end up ignoring this.

6. Put in the regression line for the linear part of the velocity graph and put in the statistics for the horizontal part of the acceleration graph. Make sure the correct part of the graph is highlighted!

7. After checking with the teacher, title the graphs and print them. 8. Look at the data values by clicking on the “Examine” button and answer questions 2-4 on

this set of graphs.

Part II: Cart pushed up a ramp 1. Raise one end of the ramp by placing a book or something under it, or by using a stand and a

clamp. 2. Place the Motion Detector at the base of the ramp so that it is pointing up the ramp. 3. Put the cart on the ramp. Make sure that the wheels of the cart are in the grooves on the

ramp. See diagram.

MotionDetector

5. Start timing. After you hear the Motion Detector clicking, give the cart a quick push so that

it gets to within 10 cm of the raised end. Don't let the cart slam into the bottom of the ramp! (This may take a few trials.)

6. Make sure your graph shows the cart going up and down the ramp. There will definitely be some “weirdness” in the graphs on either side of this motion and we will end up ignoring this. Sketch the position, velocity and acceleration graphs in the space below. Make sure you label the graphs, and include the slope of the velocity graph.

slope = _________

Questions: 1. Since you put the motion detector on the ground, what are the directions of each of the following:

positive velocity:____________ negative velocity:____________ positive acceleration:____________ negative acceleration:____________

ABRHS PHYSICS (CP) NAME: _______________

Lab 2-7: Up and Down

side 2

Answer the following right on the printed out graph: 2. Identify the region where the ball was being pushed/tossed, but still in your hands. Label this

region on the velocity and the acceleration graphs. 3. Identify the regions where the ball was “in free fall.” (This means that the cart/ball was moving

under the influence of gravity only and you were not touching it.) a. On each of the three graphs, label where the ball was moving upwards. b. On each of the three graphs, label where the ball was moving downward.

4. Determine the position, velocity and acceleration at the following points: a. On the velocity graph, locate the maximum velocity just as the ball was released. Mark and

record its value on the graph. b. On the position graph, locate the maximum height of the ball. Mark the spot on the graph

and record its value on the graph. c. On the velocity graph, locate where the ball was at its maximum height. Mark the spot on

the graph and record the velocity on the graph. d. On the acceleration graph, locate where the ball was at its maximum height. Mark the spot

on the graph and record the acceleration on the graph. Conclusions: 1. Was the acceleration of the ball constant while it was in the air? How do you know? If it was

constant, what was the value? 2. Was the acceleration of the cart constant while it was moving on the track after it left your hand?

How do you know? If it was constant, what was the value? 3. If you have a constant acceleration, yet have a zero velocity, what must you be doing? 4. When you toss something into the air, it goes up and down. At its maximum height, what is its

velocity and its acceleration. Give the numbers and also state the direction. 5. Can something have a constant acceleration, yet be going in one direction first and then in the

opposite direction later? 6. Both sets of graphs show an object going up and then coming down – so the cart or ball had to be

at the same height twice (once going up and once going down.) What is true about the velocities of the cart or ball when it is at the same height? What about the speeds?

7. If you throw a ball up in the air, it will take a certain amount of time to reach its maximum

height. How long would it take to fall back down to its original position?


Ball Toss Concept Sheet

side 1

On the surface of the earth, the acceleration due to gravity is about 10 m/s2. Ignoring air resistance, this means that all objects speed up (or slow down) at a constant rate of 10 m/s/s. On this sheet, you will calculate and draw the position of a ball that is tossed up in the air with an initial speed of 60 m/s.

1. Calculate the speed of the ball object for each second of its flight for the first 6 seconds. Record your answers in the column marked “Speed.” (Show your work below the chart.)

2. Calculate the height of the ball for each second. Record the answers in the “Height” column of the chart below. (Show your work below the chart.)

3. For each of the calculated values, draw a ball next to the appropriate height in the diagram. Label it with the appropriate time and speed. (The initial position is already done.)

4. Draw in arrows that could represent the velocity of the ball at each moment.

5. Answer the questions on the back of this sheet.

Time (s)

Speed (m/s)

Height (m)

0 60 0

1

2

3

4

5

6

180

t = 0

60 m/s

20

40

60

80

120

140

160

100


Ball Toss Concept Sheet

side 2

Questions: 1. What happened to the spacing between the balls as it got higher in the air? Explain why this

happened. 2. What do you think would have happened to the ball after the 6 seconds shown? 3. What will always be true about the speed of a tossed object when it is at its maximum height? 4. For a ball tossed up with an initial speed of 60 m/s, how fast would it be going after 1.5 seconds? 5. If the ball was thrown up with an initial speed of only 30 m/s, how high would it have gone? To answer the rest of these questions, you will also need your “Free Fall Concept Sheet.” Compare the speeds and positions of the ball in the two diagrams. 6. When putting the two pictures next to each other, what do you notice about the positions of the

ball? 7. What do you notice about the speeds of the ball at each height? 8. What would be true about the velocities of the ball at each height? 9. Why do you think I chose to start the ball toss with an initial speed of 60 m/s? (Hint: how do you

think the two concept sheets are connected?) 10. Imagine you throw a ball up with some initial speed and then catch when it gets back to your

hand a. How does the time it takes the ball to go up compare to the time it takes to fall back down? b. What is true about the speed of the ball at its maximum height? c. What is true about the speed of the ball when it gets back to your hand?


Ball Toss Problems

side 1

1. Jan throws a ball straight up in the air with an initial velocity of 20 m/s. a. How long will it take the ball to reach its highest point? b. What is the average speed of the ball while it goes up? c. What is the maximum height reached by the ball? d. How many total seconds is the ball in the air?

2. Your friend, Cindy, is playing soccer, and you see her kick the ball straight up in the air. It takes 3.5 seconds for the ball to reach its highest point. a. What was the initial velocity of the ball? b. What is the maximum height reached by the ball? c. What is the total time the ball is in the air? d. What is the velocity of the ball just it reaches the ground again?

3. Greg is playing golf and he accidentally hits the golf ball straight up in the air with an initial

velocity of 42 m/s. a. How long does it take the ball to reach its highest point? b. What is the maximum height reached by the ball? c. After only 1.5 seconds, what is the velocity of the ball? d. What is the acceleration of the ball at its highest point?

4. Peter throws a pen straight up in the air with some initial velocity. 2.3 seconds later, it has a velocity of 17 m/s. a. What was the initial velocity of the pen?


Ball Toss Problems

side 2

b. What is the maximum height reached by the pen. c. What is the velocity of the pen 6 seconds after it was thrown?

5. Marsha tosses a football straight up in the air, and then catches it 5 seconds later. (She catches

it at the same height from which it was tossed.) a. How many seconds does it take the ball to reach its maximum height? b. What was the initial velocity of the ball? c. What was the maximum height of the ball?

*6. Bobby tosses a stuffed animal straight up in the air, and then catches it 3.2 seconds later. What is the maximum height reached by the stuffed animal?

*7. Alice has a tennis ball that she throws straight up. The tennis ball reaches a maximum height of

30 meters above its release point. a. How long would it take the tennis ball to fall back down from its maximum height? b. How long did it take the ball to reach this maximum height? c. What was the initial velocity of the ball?

*8. A rock is fired down off a cliff that is 77 meters high with some initial speed. After 3.2 seconds it hits the ground. What was its initial speed?

Answers: 1. a) 2 s b) 10 m/s c) 20 m d) 4 s 2. a) 35 m/s b) 61.3 m c) 7 s d) –35 m/s 3. a) 4.2 s b) 88.2 m c) 27 m/s d) –10 m/s2 4. a) 40 m/s b) 80 m c) –20 m/s 5. a) 2.5 s b) 25 m/s c) 31.25 m 6) 12.8 m 7. a) 2.45 s b) 2.45 s c) 24.5 m/s 8) 8.1 m/s


Lab 2-8: The Acceleration of a Bouncing Ball

side 1

Purpose: To determine the acceleration of a racquetball while it is bouncing. Materials: 1 racquetball 1 photogate 1 stand 1 clamp Procedure:

1. Arrange the photogate so that the light beam is just above the top of the ball when the ball is on the table.

2. Start Logger Pro and open up the file “Experiments/Probes & Sensors/Photogates/Bounce.cmbl.”

3. Double-click on the column marked “Velocity” and in the equation, change the “0.1” to the actual diameter of your raquetball (which is 0.057 meters.)

4. Click on the “Collect” button, and then carefully drop the racquetball so that it falls in the beam of the photogate and catch it so that it only bounces once. Please make sure to not drop the ball on the photogate.

5. Record the speeds and time in the data table below. Data:

Speed of ball just before hitting the table

Speed of ball just after hitting the table

Time ball was in contact with the table Conclusions: 1. Which direction do you want call positive? What were the initial and final velocities of the ball? Up = ____________ vi = ____________ vf = ____________ 2. What was the acceleration of the racquetball as it fell? How do you know? 3. How did Logger Pro calculate the speeds of the ball? 4. What was the change in velocity of the ball? Give the magnitude as well as the direction. 5. What was the acceleration of the ball while it was in contact with the table and bouncing? 6. How many times greater than gravity was the acceleration during the bounce? 7. Why was it wrong to just subtract the two speeds to answer question 3 above?


Lab 2-8: The Acceleration of a Bouncing Ball

side 2

Follow-Up Questions: 1. A ball of clay hits the ground with a speed of 2 m/s. It doesn’t bounce, but “splats” to a stop in

only 0.04 seconds. a. What was the change in velocity of the clay? (Magnitude & direction.) b. What was the acceleration of the clay while splatting? (Magnitude & direction.)

2. A ball hits the ground with a speed of 6.5 m/s and bounces back up with a speed of 5.0 m/s. The

actual bounce only lasted for 0.004 seconds. a. What was the change in velocity of the ball during the bounce? (Magnitude & direction.) b. What was the acceleration of the ball while in contact with the ground? (Magnitude &

direction.) 3. You throw ball at a wall with a speed of 15 m/s. During the bounce off the wall, the ball has an

acceleration of 2400 m/s2 for 0.008 seconds. a. In what direction is the acceleration? How do you know? b. What is the velocity of the ball come as it comes back at you?

4. A basketball hits the ground with a speed of 12 m/s and bounces back up with a speed of 9 m/s.

If the bounce lasted 0.003 seconds, what was the acceleration of the basketball during the bounce? (Magnitude & direction.)

*5. A super ball is dropped from a height of 12 meters, hits the ground and bounces up. During the

actual bounce, the acceleration of the ball was 3700 m/s2 and the bounce lasted for 0.007 seconds. How high does the ball go after the bounce?

Answers: 1. a) 2 m/s up b) 50 m/s2 up 2. a) 11.5 m/s up b) 2875 m/s2 up 3. a) Away from wall b) –4.2 m/s 4) 7000 m/s2 up 5) 5.4 m


Acceleration Due to Gravity Problems

side 1

1. If you drop a pencil how fast is it going after 0.35 seconds? 2. If you drop a rock, how long does it take to reach a speed of 17 m/s? 3. Imagine you throw a tennis ball straight up with a speed of 25 m/s, and you end up catching it at

the same height from which you released it. a. How long would it take to reach its maximum height? b. What is its velocity after 2 seconds? c. What is its velocity after 4 seconds? d. How long was the tennis ball in the air?

4. Imagine a kangaroo jumps straight up in the air and it is in the air for a total of 1.8 seconds. a. How many seconds does it take for the kangaroo to reach its maximum height? b. What was the initial velocity of the kangaroo?

5. Sally fires an arrow straight down off a bridge with an initial speed of 35 m/s. It hits the ground after 2.2 seconds. a. How fast is it going when it hits the ground? b. How long would it take to reach a speed of 40 m/s?

6. Now Sally fires an arrow straight up with an initial speed of 35 m/s. a. How fast is it going after 2.2 seconds?


Acceleration Due to Gravity Problems

side 2

b. How long would it take to reach its maximum height? c. How long would it take to have a speed of 20 m/s, but be coming down? d. After 4.7 seconds, what is its velocity?

7. An apple falls from a tall tree and hits the ground after 1.3 seconds. How fast is it going just as it hits the ground?

8. Billy throws a paint brush straight up in the air. It reaches its maximum height after 1.9 seconds.

How fast did Billy throw the brush? 9. Sally throws a volleyball straight up with an initial speed of 17 m/s. How high does it go? 10. An acorn falls out of a tree from a height of 25 meters. How fast is it going when it hits the ground? Answers: 1) 3.5 m/s 2) 1.7 s 3. a) 2.5 s b) 5 m/s (up) c) –15 m/s (down) d) 5 s 4. a) 0.9 s b) 9 m/s 5. a) 57 m/s b) 0.5 s 6. a) 13 m/s b) 3.5 s c) 5.5 s d) –12 m/s 7) 13 m/s 8) 19 m/s 9) 14.5 m 10) 22.4 m/s

ABRHS P Chapter 2.5-2.9: Linear Motion...

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