Question: You throw a baseball straight up in

> A movie stuntwoman drops from a helicopter that is 30.0 m above the ground and moving with a constant velocity whose components are 10.0 m/s upward and 15.0 m/s horizontal and toward the south. Ignore air resistance. (a) Where on the ground (relative to

> In fighting forest fires, airplanes work in support of ground crews by dropping water on the fires. For practice, a pilot drops a canister of red dye, hoping to hit a target on the ground below. If the plane is flying in a horizontal path 90.0 m above th

> Birds of prey typically rise upward on thermals. The paths these birds take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume that a bird completes a circle of radius 6.00 m ev

> A sly 1.5-kg monkey and a jungle veterinarian with a blow-gun loaded with a tranquilizer dart are 25 m above the ground in trees 70 m apart. Just as the veterinarian shoots horizontally at the monkey, the monkey drops from the tree in a vain attempt to e

> A bird flies in the xy-plane with a velocity vector given by v =(a - bt2)

> From the top of a tall building, you throw one ball straight up with speed v0 and one ball straight down with speed v0. (a) Which ball has the greater speed when it reaches the ground? (b) Which ball gets to the ground first? (c) Which ball has a greater

> A test rocket starting from rest at point A is launched by accelerating it along a 200.0-m incline at 1.90 m/s2 (Fig. P3.43). The incline rises at 35.0° above the horizontal, and at the instant the rocket leaves it, the engines turn off and th

> The position of a dragonfly that is flying parallel to the ground is given as a function of time by r = [2.90 m +(0.0900 m/s2)t2]

> If r = bt2

> A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rocket’s acceleration has components ax(t)= at2 and ay(t)= b - gt, where a = 2.50 m/s4, b = 9.00 m/s2, and g = 1.40 m/s3. At t = 0 the rocket is at the origi

> A rocket is fired at an angle from the top of a tower of height h0 = 50.0 m. Because of the design of the engines, its position coordinates are of the form x1t2= A + Bt2 and y(t) = C + Dt3, where A, B, C, and D are constants. The acceleration of the rock

> The velocity of blood in the aorta can be measured directly with ultrasound techniques. A typical graph of blood velocity versus time during a single heartbeat is shown in Fig. P2.92. Which statement is the best interpretation of this graph? (a) The bloo

> Individuals vary considerably in total lung volume. Figure P1.94 shows the results of measuring the total lung volume and average alveolar volume of six individuals. From these data, what can you infer about the relationship among alveolar size, total lu

> If we assume that alveoli are spherical, what is the diameter of a typical alveolus? (a) 0.20 mm; (b) 2 mm; (c) 20 mm; (d) 200 mm.

> What is total volume of the gas-exchanging region of the lungs? (a) 2000 mm3; (b) 2 m3; (c) 2.0 L; (d) 120 L.

> If the aorta (diameter da) branches into two equal-sized arteries with a combined area equal to that of the aorta, what is the diameter of one of the branches? (a) √

> If you know the initial position and initial velocity of a vehicle and have a record of the acceleration at each instant, can you compute the vehicle’s position after a certain time? If so, explain how this might be done.

> If the contraction of the left ventricle lasts 250 ms and the speed of blood flow in the aorta (the large artery leaving the heart) is 0.80 m/s at the end of the contraction, what is the average acceleration of a red blood cell as it leaves the heart? (a

> A large number of seeds are observed, and their initial launch angles are recorded. The range of projection angles is found to be -51° to 75°, with a mean of 31°. Approximately 65% of the seeds are launched between 6° and 56°. (See W. J. Garrison et al.,

> If a seed is launched at an angle of 0° with the maximum initial speed, how far from the plant will it land? Ignore air resistance, and assume that the ground is flat. (a) 20 cm; (b) 93 cm; (c) 2.2 m; (d) 4.6 m.

> About how long does it take a seed launched at 90° at the highest possible initial speed to reach its maximum height? Ignore air resistance. (a) 0.23 s; (b) 0.47 s; (c) 1.0 s; (d) 2.3 s.

> The experiment is designed so that the seeds move no more than 0.20 mm between photographic frames. What minimum frame rate for the high-speed camera is needed to achieve this? (a) 250 frames/s; (b) 2500 frames/s; (c) 25,000 frames/s; (d) 250,000 frames/

> A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (a) At what time after being ejected is the boulder moving at 20.0 m>s upward? (b) At what time is it moving at 20.0 m/s downward? (c) W

> A 15-kg rock is dropped from rest on the earth and reaches the ground in 1.75 s. When it is dropped from the same height on Saturn’s satellite Enceladus, the rock reaches the ground in 18.6 s. What is the acceleration due to gravity on Enceladus?

> An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point 30.0 m below its starting point 5.00 s after it leaves the thrower’s hand. Ignore air resistanc

> The rocket-driven sled Sonic Wind No. 2, used for investigating the physiological effects of large accelerations, runs on a straight, level track 1070 m (3500 ft) long. Starting from rest, it can reach a speed of 224 m/s1500 mi/h2 in 0.900 s. (a) Compute

> A hot-air balloonist, rising vertically with a constant velocity of magnitude 5.00 m/s, releases a sandbag at an instant when the balloon is 40.0 m above the ground (Fig. E2.44). After the sandbag is released, it is in free fall. (a) Compute the position

> A dripping water faucet steadily releases drops 1.0 s apart. As these drops fall, does the distance between them increase, decrease, or remain the same? Prove your answer.

> You throw a glob of putty straight up toward the ceiling, which is 3.60 m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.50 m/s. (a) What is the speed of the putty just before it strikes the c

> A juggler throws a bowling pin straight up with an initial speed of 8.20 m/s. How much time elapses until the bowling pin returns to the juggler’s hand?

> (a) If a flea can jump straight up to a height of 0.440 m, what is its initial speed as it leaves the ground? (b) How long is it in the air?

> A disoriented physics professor drives 3.25 km north, then 2.20 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement, using the method of components. In a vector-addition diagram (roughly to scale), show that th

> A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant di

> For the vectors

> A cat walks in a straight line, which we shall call the x-axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat’s motion and construct a graph of the feline’s velo

> At launch a rocket ship weighs 4.5 million pounds. When it is launched from rest, it takes 8.00 s to reach 161 km/h; at the end of the first 1.00 min, its speed is 1610 km/h. (a) What is the average acceleration (in m/s2) of the rocket (i) during the fir

> Let u be the angle that the vector A makes with the +x-axis, measured counter clockwise from that axis. Find angle u for a vector that has these components: (a) Ax = 2.00 m, Ay = -1.00 m; (b) Ax = 2.00 m, Ay = 1.00 m; (c) Ax = -2.00 m, Ay = 1.00 m; (d) A

> Compute the x- and y-components of the vectors

> (a) Does it make sense to say that a vector is negative? Why? (b) Does it make sense to say that one vector is the negative of another? Why? Does your answer here contradict what you said in part (a)?

> A spelunker is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction 45° east of south, and then 280 m at 30° east of north. After a fourth displacement, she finds herself back where she started. Use a scale drawing to de

> A postal employee drives a delivery truck along the route shown in Fig. E1.25. Determine the magnitude and direction of the resultant displacement by drawing a scale diagram. Fig. E1.25:

> For the vectors

> You are using water to dilute small amounts of chemicals in the laboratory, drop by drop. How many drops of water are in a 1.0-L bottle?

> How many times does a human heart beat during a person’s lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm3 of blood with each beat.)

> In Wagner’s opera Das Rheingold, the goddess Freia is ransomed for a pile of gold just tall enough and wide enough to hide her from sight. Estimate the monetary value of this pile. The density of gold is 19.3 g/cm3, and take its value to be about $10 per

> Four astronauts are in a spherical space station. (a) If, as is typical, each of them breathes about 500 cm3 of air with each breath, approximately what volume of air (in cubic meters) do these astronauts breathe in a year? (b) What would the diameter (i

> How many times does a typical person blink her eyes in a lifetime?

> How many gallons of gasoline are used in the United States in one day? Assume that there are two cars for every three people, that each car is driven an average of 10,000 miles per year, and that the average car gets 20 miles per gallon.

> A rather ordinary middle-aged man is in the hospital for a routine checkup. The nurse writes “200” on the patient’s medical chart but forgets to include the units. Which of these quantities could the 200 plausibly represent? The patient’s (a) mass in kil

> Express each approximation of

> A useful and easy-to-remember approximate value for the number of seconds in a year is

> With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (a) the area of the rect

> Bacteria vary in size, but a diameter of 2.0 mm is not unusual. What are the volume (in cubic centimeters) and surface area (in square millimeters) of a spherical bacterium of that size?

> (a) The recommended daily allowance (RDA) of the trace metal magnesium is 410 mg/day for males. Express this quantity in mg/day. (b) For adults, the RDA of the amino acid lysine is 12 mg per kg of body weight. How many grams per day should a 75-kg adult

> In the fall of 2002, scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the minimum amount that must be brought together to start a nuclear chain

> The following conversions occur frequently in physics and are very useful. (a) Use 1 mi = 5280 ft and 1 h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling object is 32 ft/s2. Use 1 ft = 30.48 cm to express this accele

> A certain fuel-efficient hybrid car gets gasoline mileage of 55.0 mpg (miles per gallon). (a) If you are driving this car in Europe and want to compare its mileage with that of other European cars, express this mileage in km/L 1L = liter2. Use the conver

> While driving in an exotic foreign land, you see a speed limit sign that reads 180,000 furlongs per fortnight. How many miles per hour is this? (One furlong is 1/8 mile, and a fortnight is 14 days. A furlong originally referred to the length of a plowed

> How many years older will you be 1.00 giga second from now? (Assume a 365-day year.)

> A simple pendulum (a mass swinging at the end of a string) swings back and forth in a circular arc. What is the direction of the acceleration of the mass when it is at the ends of the swing? At the midpoint? In each case, explain how you obtained your an

> A Honda Civic travels in a straight line along a road. The car’s distance x from a stop sign is given as a function of time t by the equation x(t)= at2 - bt3, where a = 1.50 m/s2 and b = 0.0500 m/s3. Calculate the average velocity of the car for each tim

> The most powerful engine available for the classic 1963 Chevrolet Corvette Sting Ray developed 360 horsepower and had a displacement of 327 cubic inches. Express this displacement in liters (L) by using only the conversions 1 L = 1000 cm3 and 1 in. = 2.5

> Starting from a pillar, you run 200 m east (the +x-direction) at an average speed of 5.0 m/s and then run 280 m west at an average speed of 4.0 m/s to a post. Calculate (a) your average speed from pillar to post and (b) your average velocity from pillar

> How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful quantity to remember.)

> According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 cm, express this volume in cubic inches.

> Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.00 mile and (b) feet in 1.00 km.

> A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.480 s. Ignore air resistance. Find (a) the height of the tabletop above the floor; (b) the horizontal distance from the edge of the table to the point whe

> A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by

> The coordinates of a bird flying in the xy-plane are given by x(t)= at and y(t)= 3.0 m - bt2, where a = 2.4 m/s and b = 1.2 m/s2. (a) Sketch the path of the bird between t = 0 and t = 2.0 s. (b) Calculate the velocity and acceleration vectors of the bird

> A dog running in an open field has components of velocity vx = 2.6 m>s and vy = -1.8 m/s at t1 = 10.0 s. For the time interval from t1 = 10.0 s to t2 = 20.0 s, the average acceleration of the dog has magnitude 0.45 m/s2 and direction 31.0° measured from

> The official’s truck in Fig. 2.2 is at x1 = 277 m at t1 = 16.0 s and is at x2 = 19 m at t2 = 25.0 s. (a) Sketch two different possible x-t graphs for the motion of the truck. (b) Does the average velocity vav-x during the time interval

> A jet plane is flying at a constant altitude. At time t1 = 0, it has components of velocity vx = 90 m/s, vy = 110 m/s. At time t2 = 30.0 s, the components are vx = -170 m/s, vy = 40 m/s. (a) Sketch the velocity vectors at t1 and t2. How do these two vect

> The position of a squirrel running in a park is given by

> An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50 mi/h) is blowing toward the south. (a) If the airspeed of the plane (its speed in still air) is 320.0 km/h (about 200 mi/h), in which direction should the pilot head? (b) What is the

> Canada geese migrate essentially along a north–south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. If one goose is flying at 100 km>h relative to the air but a 40-km/h wind is blowing from west to

> (a) In which direction should the motorboat in Exercise 3.35 head to reach a point on the opposite bank directly east from your starting point? (The boat’s speed relative to the water remains 4.2 m/s.) (b) What is the velocity of the boat relative to the

> A river flows due south with a speed of 2.0 m/s. You steer a motorboat across the river; your velocity relative to the water is 4.2 m/s due east. The river is 500 m wide. (a) What is your velocity (magnitude and direction) relative to the earth? (b) How

> The nose of an ultra-light plane is pointed due south, and its airspeed indicator shows 35 m/s. The plane is in a 10-m/s wind blowing toward the southwest relative to the earth. (a) In a vector addition diagram, show the relationship of

> A canoe has a velocity of 0.40 m/s southeast relative to the earth. The canoe is on a river that is flowing 0.50 m/s east relative to the earth. Find the velocity (magnitude and direction) of the canoe relative to the river.

> Two piers, A and B, are located on a river; B is 1500 m downstream from A (Fig. E3.32). Two friends must make round trips from pier A to pier B and return. One rows a boat at a constant speed of 4.00 km/h relative to the water; the other walks on the sho

> A “moving sidewalk” in an airport terminal moves at 1.0 m>s and is 35.0 m long. If a woman steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does it take her to reach the opposite end if she walks (a) in the same dir

> Can you find two vectors with different lengths that have a vector sum of zero? What length restrictions are required for three vectors to have a vector sum of zero? Explain.

> A railroad flatcar is traveling to the right at a speed of 13.0 m>s relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar (Fig. E3.30). What is the velocity (magnitude and direction) of the scooter relative t

> A web page designer creates an animation in which a dot on a computer screen has position (a) Find the magnitude and direction of the dot’s average velocity between t = 0 and t = 2.0 s. (b) Find the magnitude and direction of the instan

> At its Ames Research Center, NASA uses its large “20-G” centrifuge to test the effects of very large accelerations (“hyper gravity”) on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an ast

> The radius of the earth’s orbit around the sun (assumed to be circular) is 1.50 × 108 km, and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth, in m/s? (b) What is the radial acceleration of

> A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center (Fig. E3.27). The linear speed of a passenger on the rim is constant and equal to 6.00 m/s. What are the magnitude and direction of the passenger’s

> A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. (a) What is the linear speed of the blade tip, in m/s? (b) What is the radial acceleration of t

> A jet plane comes in for a downward dive as shown in Fig. E3.25. The bottom part of the path is a quarter circle with a radius of curvature of 280 m. According to medical tests, pilots will lose consciousness when they pull out of a dive at an upward acc

> Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this fluid, causing dizziness. Suppose that a skater is spinning very fast at 3.0 revolutions per second about a vertical axis through the center of

> The earth has a radius of 6380 km and turns around once on its axis in 24 h. (a) What is the radial acceleration of an object at the earth’s equator? Give your answer in m/s2 and as a fraction of g. (b) If arad at the equator is greater than g, objects w

> A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of 20.0 m/s. A 1.0-kg stone is thrown from the basket with an initial velocity of 15.0 m/s perpendicular to the path of the descending balloon, as measured relative

> Can you have zero velocity and nonzero average acceleration? Zero velocity and nonzero acceleration? Use a vx-t graph to explain, and give an example of such motion.

> A man stands on the roof of a 15.0-m-tall building and throws a rock with a speed of 30.0 m/s at an angle of 33.0° above the horizontal. Ignore air resistance. Calculate (a) the maximum height above the roof that the rock reaches; (b) the speed of the ro

> Firemen use a high-pressure hose to shoot a stream of water at a burning building. The water has a speed of 25.0 m/s as it leaves the end of the hose and then exhibits projectile motion. The firemen adjust the angle of elevation a of the hose until the w

> A rhinoceros is at the origin of coordinates at time t1 = 0. For the time interval from t1 = 0 to t2 = 12.0 s, the rhino’s average velocity has x-component -3.8 m/s and y-component 4.9 m/s. At time t2 = 12.0 s, (a) what are the x- and y-coordinates of th

> In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin

> A shot putter releases the shot some distance above the level ground with a velocity of 12.0 m/s, 51.0° above the horizontal. The shot hits the ground 2.08 s later. Ignore air resistance. (a) What are the components of the shot’s acceleration while in fl

> A major leaguer hits a baseball so that it leaves the bat at a speed of 30.0 m/s and at an angle of 36.9° above the horizontal. Ignore air resistance. (a) At what two times is the baseball at a height of 10.0 m above the point at which it left the bat? (

> On level ground a shell is fired with an initial velocity of 40.0 m>s at 60.0° above the horizontal and feels no appreciable air resistance. (a) Find the horizontal and vertical components of the shell’s initial velocity. (b) How long does it take the sh