Solved: A ball is dropped from the roof of a tall building

Problem 1CQ a. Write a paragraph describing the particle model. What is it, and why is it important? b. Give two examples of situations, different from those described in the text, for which the particle model is appropriate. c. Give an example of a situation, different from those described in the text, for which it would be inappropriate.

Problem 1P You’ve made a video of a car as it skids to a halt to avoid hitting an object in the road. Use the images from the video to draw a motion diagram of the car from the time the skid begins until the car is stopped.

Problem 2CQ A softball player slides into second base. Use the particle model to draw a motion diagram of the player from the time he begins to slide until he reaches the base. Number the dots in order, starting with zero.

Problem 2P A man rides a bike along a straight road for 5 min, then has a flat tire. He stops for 5 min to repair the flat, but then realizes he cannot fix it. He continues his journey by walking the rest of the way, which takes him another 10 min. Use the particle model to draw a motion diagram of the man for the entire motion described here. Number the dots in order, starting with zero.

Problem 3CQ A car travels to the left at a steady speed for a few seconds, then brakes for a stop sign. Use the particle model to draw a motion diagram of the car for the entire motion described here. Number the dots in order, starting with zero.

Problem 3P A jogger running east at a steady pace suddenly develops a cramp. He is lucky: A westbound bus is sitting at a bus stop just ahead. He gets on the bus and enjoys a quick ride home. Use the particle model to draw a motion diagram of the jogger for the entire motion described here. Number the dots in order, starting with zero.

Problem 4CQ A ball is dropped from the roof of a tall building and students in a physics class are asked to sketch a motion diagram for this situation. A student submits the diagram shown in Figure Q1.4 . Is the diagram correct? Explain. Reference: Figure 1.4:

Figure P1.4 shows Sue between her home and the cinema. What is Sue’s position x if a. Her home is the origin? b. The cinema is the origin?

Problem 5CQ Write a sentence or two describing the difference between position and displacement. Give one example of each.

Problem 5P Keira starts at position x = 23 m along a coordinate axis. She then undergoes a displacement of -45 m. What is her final position?

Problem 6CQ Give an example of a trip you might take in your car for which the distance traveled as measured on your car’s odometer is not equal to the displacement between your initial and final positions.

Problem 6P A car travels along a straight east-west road. A coordinate system is established on the road, with x increasing to the east. The car ends up 14 mi west of the origin, which is defined as the intersection with Mulberry Road. If the car’s displacement was -23 mi, what side of Mulberry Road did the car start on? How far from the intersection was the car at the start?

Problem 7CQ Write a sentence or two describing the difference between speed and velocity. Give one example of each.

Problem 7P Foraging bees often move in straight lines away from and toward their hives. Suppose a bee starts at its hive and flies 500 m due east, then flies 400 m west, then 700 m east. How far is the bee from the hive?

Problem 8CQ The motion of a skateboard along a horizontal axis is observed for 5 s. The initial position of the skateboard is negative with respect to a chosen origin, and its velocity throughout the 5 s is also negative. At the end of the observation time, is the skateboard closer to or farther from the origin than initially? Explain.

Problem 8P A security guard walks at a steady pace, traveling 110 m in one trip around the perimeter of a building. It takes him 240 s to make this trip. What is his speed?

Problem 9CQ Can the velocity of an object be positive during a time interval in which its position is always negative? Can its velocity be positive during a time interval in which its displacement is negative?

Problem 9P List the following items in order of decreasing speed, from greatest to least: (i) A wind-up toy car that moves 0.15 m in 2.5 s. (ii) A soccer ball that rolls 2.3 m in 0.55 s. (iii) A bicycle that travels 0.60 m in 0.075 s. (iv) A cat that runs 8.0 m in 2.0 s.

Problem 10CQ Two friends watch a jogger complete a 400 m lap around the track in 100 s. One of the friends states, “The jogger’s velocity was 4 m/s during this lap.” The second friend objects, saying, “No, the jogger’s speed was 4 m/s.” Who is correct? Justify your answer.

Problem 10P Figure P1.10 shows the motion diagram for a horse galloping in one direction along a straight path. Not every dot is labeled, but the dots are at equally spaced instants of time. What is the horse’s velocity a. During the first ten seconds of its gallop? b. During the interval from 30 s to 40 s? c. During the interval from 50 s to 70 s?

Problem 11CQ A softball player hits the ball and starts running toward first base. Draw a motion diagram, using the particle model, showing her velocity vectors during the first few seconds of her run.

Problem 11P It takes Harry 35 s to walk from x = -12 m to x = -47 m. What is his velocity?

Problem 12CQ A child is sledding on a smooth, level patch of snow. She encounters a rocky patch and slows to a stop. Draw a motion diagram, using the particle model, showing her velocity vectors.

Problem 12P A dog trots from x = -12 m to x = 3 m in 10 s. What is its velocity?

Problem 13CQ A skydiver jumps out of an airplane. Her speed steadily increases until she deploys her parachute, at which point her speed quickly decreases. She subsequently falls to earth at a constant rate, stopping when she lands on the ground. Draw a motion diagram, using the particle model, that shows her position at successive times and includes velocity vectors.

Problem 13P A ball rolling along a straight line with velocity 0.35 m/s goes from x = 2.1 m to x = 7.3 m. How much time does this take?

Problem 14CQ Your roommate drops a tennis ball from a third-story balcony. It hits the sidewalk and bounces as high as the second story. Draw a motion diagram, using the particle model, showing the ball’s velocity vectors from the time it is released until it reaches the maximum height on its bounce.

Problem 14P Convert the following to SI units: a. 9.12 ?s b. 3.42 km c. 44 cm/ms d. 80 km/h

Problem 15CQ A car is driving north at a steady speed. It makes a gradual 90° left turn without losing speed, then continues driving to the west. Draw a motion diagram, using the particle model, showing the car’s velocity vectors as seen from a helicopter hovering over the highway.

Problem 15P Convert the following to SI units: a. 8.0 in b. 66 ft/s c. 60 mph

Problem 16CQ A toy car rolls down a ramp, then across a smooth, horizontal floor. Draw a motion diagram, using the particle model, showing the car’s velocity vectors.

Problem 16P Convert the following to SI units: a. 1.0 hour b. 1.0 day c. 1.0 year

Problem 17CQ Estimate the average speed with which you go from home to campus (or another trip you commonly make) via whatever mode of transportation you use most commonly. Give your answer in both mph and m/s. Describe how you arrived at this estimate.

Problem 17P List the following three speeds in order, from smallest to largest: 1 mm per ?s, 1 km per ks, 1 cm per ms.

Problem 18CQ Estimate the number of times you sneezed during the past year. Describe how you arrived at this estimate.

Problem 18P How many significant figures does each of the following numbers have? a. 6.21 b. 62.1 c. 0.620 d. 0.062

Problem 19CQ Density is the ratio of an object’s mass to its volume. Would you expect density to be a vector or a scalar quantity? Explain.

Problem 19P How many significant figures does each of the following numbers have? a. 0.621 b. 0.006200 c. 1.0621

Problem 20MCQ A student walks 1.0 mi west and then 1.0 mi north. Afterward, how far is she from her starting point? A. 1.0 mi B. 1.4 mi C. 1.6 mi D. 2.0 mi

Problem 20P Compute the following numbers to three significant figures.

Problem 21MCQ Which of the following motions is described by the motion diagram of Figure Q1.21 ? A. An ice skater gliding across the ice. B. An airplane braking to a stop after landing. C. A car pulling away from a stop sign. D. A pool ball bouncing off a cushion and reversing direction.

Problem 21P The Empire State Building has a height of 1250 ft. Express this height in meters, giving your result in scientific notation with three significant figures.

Problem 22MCQ A bird flies 3.0 km due west and then 2.0 km due north. What is the magnitude of the bird’s displacement? A. 2.0 km B. 3.0 km C. 3.6 km D. 5.0 km

Problem 22P Estimate (don’t measure!) the length of a typical car. Give your answer in both feet and meters. Briefly describe how you arrived at this estimate.

Problem 23MCQ A bird flies 3.0 km due west and then 2.0 km due north. Another bird flies 2.0 km due west and 3.0 km due north. What is the angle between the net displacement vectors for the two birds? A. 23° B. 34° C. 56° D. 90°

Problem 23P Blades of grass grow from the bottom, so, as growth occurs, the top of the blade moves upward. During the summer, when your lawn is growing quickly, estimate this speed, in m/s. Make this estimate from your experience noting, for instance, how often you mow the lawn and what length you trim. Express your result in scientific notation.

Problem 24MCQ A woman walks briskly at 2.00 m/s. How much time will it take her to walk one mile? A. 8.30 min B. 13.4 min C. 21.7 min D. 30.0 min

Problem 24P Estimate the average speed with which the hair on your head grows. Give your answer in both m/s and ?m/h. Briefly describe how you arrived at this estimate.

Problem 25MCQ Compute 3.24 m + 0.532 m to the correct number of significant figures. A. 3.7 m B. 3.77 m C. 3.772 m D. 3.7720 m

Problem 25P Estimate the average speed at which your fingernails grow, in both m/s and ?m/h. Briefly describe how you arrived at this estimate.

Problem 26MCQ A rectangle has length 3.24 m and height 0.532 m. To the correct number of significant figures, what is its area?

Problem 26P Carol and Robin share a house. To get to work, Carol walks north 2.0 km while Robin drives west 7.5 km. How far apart are their workplaces?

Problem 27MCQ The earth formed years ago. What is this time in seconds?

Problem 27P Joe and Max shake hands and say goodbye. Joe walks east 0.55 km to a coffee shop, and Max flags a cab and rides north 3.25 km to a bookstore. How far apart are their destinations?

Problem 28MCQ An object’s average density r is defined as the ratio of its mass to its volume: . The earth’s mass is , and its volume is . What is the earth’s average density?

Problem 28P A city has streets laid out in a square grid, with each block 135 m long. If you drive north for three blocks, then west for two blocks, how far are you from your starting point?

Problem 29P A butterfly flies from the top of a tree in the center of a garden to rest on top of a red flower at the garden’s edge. The tree is 8.0 m taller than the flower, and the garden is 12 m wide. Determine the magnitude of the butterfly’s displacement.

A garden has a circular path of radius 50 m. John starts at the easternmost point on this path, then walks counterclockwise around the path until he is at its southernmost point. What is John’s displacement? Use the (magnitude, direction) notation for your answer.

Problem 31P Migrating geese tend to travel at approximately constant speed, flying in segments that are straight lines. A goose flies 32 km south, then turns to fly 20 km west. Afterward, how far is the goose from its original position?

Problem 32P A ball on a porch rolls 60 cm to the porch’s edge, drops 40 cm, continues rolling on the grass, and eventually stops 80 cm from the porch’s edge. What is the magnitude of the ball’s net displacement, in centimeters?

Problem 33P A kicker punts a football from the very center of the field to the sideline 43 yards downfield. What is the net displacement of the ball? (A football field is 53 yards wide.)

Problem 34GP Problem is motion problem similar to this you will learn to solve in Chapter 2. For now, simply interpret the problem by drawing a motion diagram showing the object’s position and its velocity vectors. Do not solve these problems or do any mathematics. In a typical greyhound race, a dog accelerates to a speed of 20 m/s over a distance of 30 m. It then maintains this speed. What would be a greyhound’s time in the 100 m dash?

Problem 35GP Problem is motion problem similar to this you will learn to solve in Chapter 2. For now, simply interpret the problem by drawing a motion diagram showing the object’s position and its velocity vectors. Do not solve these problems or do any mathematics. Billy drops a watermelon from the top of a three-story building, 10 m above the sidewalk. How fast is the watermelon going when it hits?

Problem 36GP Sam is recklessly driving 60 mph in a 30 mph speed zone when he suddenly sees the police. He steps on the brakes and slows to 30 mph in three seconds, looking nonchalant as he passes the officer. How far does he travel while braking?

Problem 37GP A speed skater moving across frictionless ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is her acceleration on the rough ice?

Problem 38GP The giant eland, an African antelope, is an exceptional jumper, able to leap 1.5 m off the ground. To jump this high, with what speed must the eland leave the ground?

Problem 39GP A ball rolls along a smooth horizontal floor at 10 m/s, then starts up a 20° ramp. How high does it go before rolling back down?

Problem 40GP A motorist is traveling at 20m/s. He is 60 m from a stop light when he sees it turn yellow. His reaction time, before stepping on the brake, is 0.50 s. What steady deceleration while braking will bring him to a stop right at the light?

Problem 42GP Problem show a motion diagram. For each of these problems, write a one or two sentence “story” about a real object that has this motion diagram. Your stories should talk about people or objects by name and say what they are doing. Problems 39 through 45 are examples of motion short stories.

Problem 41GP Problem show a motion diagram. For each of these problems, write a one or two sentence “story” about a real object that has this motion diagram. Your stories should talk about people or objects by name and say what they are doing. Problems 39 through 45 are examples of motion short stories.

Problem 43GP Problem show a motion diagram. For each of these problems, write a one or two sentence “story” about a real object that has this motion diagram. Your stories should talk about people or objects by name and say what they are doing. Problems 39 through 45 are examples of motion short stories.

Problem 44GP Problem show a motion diagram. For each of these problems, write a one or two sentence “story” about a real object that has this motion diagram. Your stories should talk about people or objects by name and say what they are doing. Problems 39 through 45 are examples of motion short stories.

Problem 45GP Problems show a motion diagram. For each of these problems, write a one or two sentence “story” about a real object that has this motion diagram. Your stories should talk about people or objects by name and say what they are doing. Problems 34 through 40 are examples of motion short stories. FIGURE 45

Problem 46GP Problem show a motion diagram. For each of these problems, write a one or two sentence “story” about a real object that has this motion diagram. Your stories should talk about people or objects by name and say what they are doing. Problems 39 through 45 are examples of motion short stories.

Problem 47GP How many inches does light travel in one nanosecond? The speed of light is .

Problem 48GP Joseph watches the roadside mile markers during a long car trip on an interstate highway. He notices that at 10:45 am they are passing a marker labeled 101, and at 11:00 am the car reaches marker 119. What is the car’s speed, in mph?

Problem 49GP Alberta is going to have dinner at her grandmother’s house, but she is running a bit behind schedule. As she gets onto the highway, she knows that she must exit the highway within 45 min if she is not going to arrive late. Her exit is 32 mi away. What is the slowest speed at which she could drive and still arrive in time? Express your answer in miles per hour.

Problem 50GP The end of Hubbard Glacier in Alaska advances by an average of 105 feet per year. What is the speed of advance of the glacier in m/s?

Problem 51GP The earth completes a circular orbit around the sun in one year. The orbit has a radius of 93,000,000 miles. What is the speed of the earth around the sun in m/s? Report your result using scientific notation.

Problem 52GP Shannon decides to check the accuracy of her speedometer. She adjusts her speed to read exactly 70 mph on her speedometer and holds this steady, measuring the time between successive mile markers separated by exactly 1.00 mile. If she measures a time of 54 s, is her speedometer accurate? If not, is the speed it shows too high or too low?

Problem 53GP Motor neurons in mammals transmit signals from the brain to skeletal muscles at approximately 25 m/s. Estimate how much time in ms it will take for a signal to get from your brain to your hand.

Problem 54GP Satellite data taken several times per hour on a particular albatross showed travel of 1200 km over a time of 1.4 days. a. Given these data, what was the bird’s average speed in mph? b. Data on the bird’s position were recorded only intermittently. Explain how this means that the bird’s actual average speed was higher than what you calculated in part a.

Problem 55GP Your brain communicates with your body using nerve impulses, electrical signals propagated along axons. Axons come in two varieties: insulated axons with a sheath made of myelin, and uninsulated axons with no such sheath. Myelinated (sheathed) axons conduct nerve impulses much faster than unmyelinated (unsheathed) axons. The impulse speed depends on the diameter of the axons and the sheath, but a typical myelinated axon transmits nerve impulses at a speed of about 25 m/s, much faster than the typical 2.0 m/s for an unmyelinated axon. Figure 55 shows three equal-length nerve fibers consisting of eight axons in a row. Nerve impulses enter at the left side simultaneously and travel to the right. a. Draw motion diagrams for the nerve impulses traveling along fibers A, B, and C. ________________ b. Which nerve impulse arrives at the right side first? ________________ c. Which will be last? FIGURE 55

Problem 56GP The bacterium Escherichia coli (or E. coli) is a single celled organism that lives in the gut of healthy humans and animals. Its body shape can be modeled as a 2-?m-long cylinder with a 1 ?m diameter, and it has a mass of . Its chromosome consists of a single double-stranded chain of DNA 700 times longer than its body length. The bacterium moves at a constant speed of 20 ?m/s, though not always in the same direction. Answer the following questions about E. coli using SI units (unless specifically requested otherwise) and correct significant figures. a. What is its length? b. Diameter? c. Mass? d. What is the length of its DNA, in millimeters? e. If the organism were to move along a straight path, how many meters would it travel in one day?

Problem 57GP The bacterium Escherichia coli (or E. coli) is a single celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, it swims along zigzag paths at a constant speed changing direction at varying time intervals. Figure P1.61 shows the positions of an E. coli as it moves from point A to point J. Each segment of the motion can be identified by two letters, such as segment BC. During which segments, if any, does the bacterium have the same a. Displacement? b. Speed? c. Velocity?

Problem 58GP In 2003, the population of the United States was 291 million people. The per-capita income was $31,459. What was the total income of everyone in the United States? Express your answer in scientific notation, with the correct number of significant figures.

Problem 59GP The sun is 30° above the horizon. It makes a 52-m-long shadow of a tall tree. How high is the tree?

Problem 60GP A large passenger aircraft accelerates down the runway for a distance of 3000 m before leaving the ground. It then climbs at a steady 3.0° angle. After the plane has traveled 3000 m along this new trajectory, (a) how high is it, and (b) how far horizontally is it, from its initial position?

Problem 61GP Starting from its nest, an eagle flies at constant speed for 3.0 min due east, then 4.0 min due north. From there the eagle flies directly to its nest at the same speed. How long is the eagle in the air?

Problem 62GP John walks 1.00 km north, then turns right and walks 1.00 km east. His speed is 1.50 m/s during the entire stroll. a. What is the magnitude of his displacement, from beginning to end? b. If Jane starts at the same time and place as John, but walks in a straight line to the endpoint of John’s stroll, at what speed should she walk to arrive at the endpoint just when John does?

Problem 63PP Growth Speed The images of trees in Figure P1.68 come from a catalog advertising fast-growing trees. If we mark the position of the top of the tree in the successive years, as shown in the graph in the figure, we obtain a motion diagram much like ones we have seen for other kinds of motion. The motion isn’t steady, of course. In some months the tree grows rapidly; in other months, quite slowly. We can see, though, that the average speed of growth is fairly constant for the first few years. What is the tree’s speed of growth, in feet per year, from t = 1 yr to t = 3 yr? A. 12 ft/yr B. 9 ft/yr C. 6 ft/yr D. 3 ft/yr

Problem 64PP Growth Speed The images of trees in Figure P1.68 come from a catalog advertising fast-growing trees. If we mark the position of the top of the tree in the successive years, as shown in the graph in the figure, we obtain a motion diagram much like ones we have seen for other kinds of motion. The motion isn’t steady, of course. In some months the tree grows rapidly; in other months, quite slowly. We can see, though, that the average speed of growth is fairly constant for the first few years. What is this speed in m/s?

Problem 65PP Growth Speed The images of trees in Figure P1.68 come from a catalog advertising fast-growing trees. If we mark the position of the top of the tree in the successive years, as shown in the graph in the figure, we obtain a motion diagram much like ones we have seen for other kinds of motion. The motion isn’t steady, of course. In some months the tree grows rapidly; in other months, quite slowly. We can see, though, that the average speed of growth is fairly constant for the first few years. At the end of year 3, a rope is tied to the very top of the tree to steady it. This rope is staked into the ground 15 feet away from the tree. What angle does the rope make with the ground? A. 63° B. 60° C. 30° D. 27°