Question: A movie stuntwoman drops from a helicopter

> Earthquakes produce several types of shock waves. The most well-known are the P-waves (P for primary or pressure) and the S-waves (S for secondary or shear). In the earth’s crust, P-waves travel at about 6.5 km/s and S-waves move at about 3.5 km/s. The t

> A lunar lander is descending toward the moon’s surface. Until the lander reaches the surface, its height above the surface of the moon is given by y(t)= b - ct + dt2, where b = 800 m is the initial height of the lander above the surface, c = 60.0 m/s, an

> A typical male sprinter can maintain his maximum acceleration for 2.0 s, and his maximum speed is 10 m/ s. After he reaches this maximum speed, his acceleration becomes zero, and then he runs at constant speed. Assume that his acceleration is constant du

> The Mars Polar Lander spacecraft was launched on January 3, 1999. On December 3, 1999, the day Mars Polar Lander impacted the Martian surface at high velocity and probably disintegrated, the positions of the earth and Mars were given by these coordinates

> You are a mechanical engineer working for a manufacturing company. Two forces, F S 1 and F S 2, act on a component part of a piece of equipment. Your boss asked you to find the magnitude of the larger of these two forces. You can vary the angle between F

> You are a team leader at a pharmaceutical company. Several technicians are preparing samples, and you want to compare the densities of the samples (density = mass>volume) by using the mass and volume values they have reported. Unfortunately, you did n

> Later in our study of physics we will encounter quantities represented by (

> You are given vectors

> Two vectors

> Prove these statements: (a) As long as you can ignore the effects of the air, if you throw anything vertically upward, it will have the same speed when it returns to the release point as when it was released. (b) The time of flight will be twice the time

> The scalar product of vectors

> Obtain a unit vector perpendicular to the two vectors given in Exercise 1.41. Exercise 1.41: Given two vectors

> Vector

> A cube is placed so that one corner is at the origin and three edges are along the x-, y-, and z-axes of a coordinate system (Fig. P1.80). Use vectors to compute (a) the angle between the edge along the z-axis (line ab) and the diagonal from the origin t

> Vectors

> In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates for which one of the C¬H bonds is in the direction of

> You are camping with Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 21.0 m from yours, in the direction 23.0° south of east. Karl’s tent is 32.0 m from yours, in the direction 37.0° north

> Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 26.0 m in a direction 60.0° west of north. Jane walks 16.0 m in a direction 30.0° south of west. They the

> A dog in an open field runs 12.0 m east and then 28.0 m in a direction 50.0° west of north. In what direction and how far must the dog then run to end up 10.0 m south of her original starting point?

> A fence post is 52.0 m from where you are standing, in a direction 37.0° north of east. A second fence post is due south from you. How far are you from the second post if the distance between the two posts is 68.0 m?

> Which of the following are legitimate mathematical operations: (a)

> While following a treasure map, you start at an old oak tree. You first walk 825 m directly south, then turn and walk 1.25 km at 30.0° west of north, and finally walk 1.00 km at 32.0° north of east, where you find the treasure: a biography of Isaac Newto

> You decide to go to your favorite neighborhood restaurant. You leave your apartment, take the elevator 10 flights down (each flight is 3.0 m), and then walk 15 m south to the apartment exit. You then proceed 0.200 km east, turn north, and walk 0.100 km t

> A physical therapy patient has a forearm that weighs 20.5 N and lifts a 112.0-N weight. These two forces are directed vertically downward. The only other significant forces on this forearm come from the biceps muscle (which acts perpendicular to the fore

> A ship leaves the island of Guam and sails 285 km at 62.0° north of west. In which direction must it now head and how far must it sail so that its resultant displacement will be 115 km directly east of Guam?

> You are lost at night in a large, open field. Your GPS tells you that you are 122.0 m from your truck, in a direction 58.0° east of south. You walk 72.0 m due west along a ditch. How much farther, and in what direction, must you walk to reach your truck?

> An explorer in Antarctica leaves his shelter during a whiteout. He takes 40 steps northeast, next 80 steps at 60° north of west, and then 50 steps due south. Assume all of his steps are equal in length. (a) Sketch, roughly to scale, the three vectors and

> As a test of orienteering skills, your physics class holds a contest in a large, open field. Each contestant is told to travel 20.8 m due north from the starting point, then 38.0 m due east, and finally 18.0 m in the direction 33.0° west of south. After

> On a training flight, a student pilot flies from Lincoln, Nebraska, to Clarinda, Iowa, next to St. Joseph, Missouri, and then to Manhattan, Kansas (Fig. P1.66). The directions are shown relative to north: 0° is north, 90° is east, 1

> You leave the airport in College Station and fly 23.0 km in a direction 34.0o south of east. You then fly 46.0 km due north. How far and in what direction must you then fly to reach a private landing strip that is 32.0 km due west of the College Station

> A sailor in a small sailboat encounters shifting winds. She sails 2.00 km east, next 3.50 km southeast, and then an additional distance in an unknown direction. Her final position is 5.80 km directly east of the starting point (Fig. P1.64). Find the magn

> An object is thrown straight up into the air and feels no air resistance. How can the object have an acceleration when it has stopped moving at its highest point?

> A patient with a dislocated shoulder is put into a traction apparatus as shown in Fig. P1.63. The pulls

> A plane leaves the airport in Galisteo and flies 170 km at 68.0° east of north; then it changes direction to fly 230 km at 36.0° south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, in

> As noted in Exercise 1.26, 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

> Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces

> Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 21.0° west of north, and the resultant of these two pulls is 460.0 N directly northward. Use vector components to find the magnitude of

> Two ropes in a vertical plane exert equal-magnitude forces on a hanging weight but pull with an angle of 72.0° between them. What pull does each rope exert if their resultant pull is 372 N directly upward?

> Estimate the number of atoms in your body.

> Biological tissues are typically made up of 98% water. Given that the density of water is 1.0 × 103 kg/m3, estimate the mass of (a) the heart of an adult human; (b) a cell with a diameter of 0.5 mm; (c) a honeybee.

> As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 ± 0.02 cm and a thickness of 0.050 ± 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume.

> A rectangular piece of aluminum is 7.60 ± 0.01 cm long and 1.90 ±0.01 cm wide. (a) Find the area of the rectangle and the uncertainty in the area. (b) Verify that the fractional uncertainty in the area is equal to the sum of the fractional uncertainties

> You run due east at a constant speed of 3.00 m/s for a distance of 120.0 m and then continue running east at a constant speed of 5.00 m/s for another 120.0 m. For the total 240.0-m run, is your average velocity 4.00 m/s, greater than 4.00 m/s, or less th

> The black dots at the top of Fig. Q2.2 represent a series of high-speed photographs of an insect flying in a straight line from left to right (in the positive x-direction). Which of the graphs in Fig. Q2.2 most plausibly depicts this insectâ€&

> The density of air under standard laboratory conditions is 1.29 kg/m3, and about 20% of that air consists of oxygen. Typically, people breathe about 1/2 L of air per breath. (a) How many grams of oxygen does a person breathe in a day? (b) If this air is

> A maser is a laser-type device that produces electromagnetic waves with frequencies in the microwave and radio-wave bands of the electromagnetic spectrum. You can use the radio waves generated by a hydrogen maser as a standard of frequency. The frequency

> In January 2006 astronomers reported the discovery of a planet, comparable in size to the earth, orbiting another star and having a mass about 5.5 times the earth’s mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. If this

> An acre has a length of one furlong (1/8 mi) and a width one-tenth of its length. (a) How many acres are in a square mile? (b) How many square feet are in an acre? See Appendix E. (c) An acre-foot is the volume of water that would cover 1 acre of flat la

> Recall that density is mass divided by volume, and consult Appendix B as needed. (a) Calculate the average density of the earth in g/cm3, assuming our planet is a perfect sphere. (b) In about 5 billion years, at the end of its lifetime, our sun will end

> 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

> You throw a baseball straight up in the air so that it rises to a maximum height much greater than your height. Is the magnitude of the ball’s acceleration greater while it is being thrown or after it leaves your hand? Explain.

> Express each approximation of

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