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physics
modern physics

University Physics With Modern Physics 2nd edition Wolfgang Bauer, Gary Westfall - Solutions

The distance from the center of the Moon to the center of the Earth ranges from approximately 356,000 km to 407,000 km.a) What is the minimum distance to the Moon in miles?b) What is the maximum distance to the Moon in miles?
1. A speed of 7 mm/u,s is equal to ___________. a) 7000 m/s b) 70 m/s c) 7 m/s d) 0.07 m/s 2. A hockey puck, whose diameter is approximately 3 inches, is to be used to determine the value of π to three significant figures by carefully measuring its diameter and its circumference. For this
In Major League baseball, the pitcher delivers his pitches from a distance of 60 feet, 6 inches from home plate. What is the distance in meters?
A flea hops in a straight path along a meter stick, starting at 0.7 cm and making successive jumps, which are measured to be 3.2 cm, 6.5 cm, 8.3 cm, 10.0 cm, 11.5 cm, and 15.5 cm. Express the answers to the following questions in scientific notation, with units of meters and an appropriate number
One cubic centimeter of water has a mass of 1 gram. A milliliter is equal to a cubic centimeter. What is the mass, in kilograms, of a liter of water? A metric ton is a thousand kilograms. How many cubic centimeters of water are in a metric ton of water? If a metric ton of water were held in a
The speed limit on a particular stretch of road is 45 miles per hour. Express this speed limit in milli furlongs per micro fortnight. A furlong is 1/8 mile, and a fortnight is a period of 2 weeks.
According to one mnemonic rhyme, "A pint's a pound, the world around." Investigate this statement of equivalence by calculating the weight of a pint of water, assuming that the density of water is 1000. kg/m3 and that the weight of 1.00 kg of a substance is 2.21 pounds. The volume of 1.00 fluid
If the radius of a planet is larger than that of Earth by a factor of 8.7, how much bigger is the surface area of the planet than Earths?
If the radius of a planet is larger than that of Earth by a factor of 5.8, how much bigger is the volume of the planet than Earth's?
What is the maximum distance from which a sailor on top of the mast of ship 1, at 34 m above the oceans surface, can see another sailor on top of the mast of ship 2, at 26 m above the ocean's surface?
You are flying in a jetliner at an altitude of 35,000 ft. How far away is the horizon?
How many cubic inches are in 1.56 barrels of oil?
A car's gasoline tank has the shape of a right rectangular box with a square base whose sides measure 62 cm. Its capacity is 52 L. If the tank has only 1.5 I. remaining, how deep is the gasoline in the tank, assuming the car is parked on level ground?
The volume of a sphere is given by the formula 4/3πr3 where r is the radius of the sphere. The average density of an object is simply the ratio of its mass to its volume. Using the numerical data found in Table 12.1, express the answers to the following questions in scientific notation, with SI
A tank is in the shape of an inverted cone, having height h = 2.5 m and base radius r = 0.75 m. If water is poured into the tank at a rate of 15 I./s, how long will it take to fill the tank?
Water flows into a cubical tank at a rate of 15 L/s. If the top surface of the water in the tank is rising by 1.5 cm every second, what is the length of each side of the tank?
The atmosphere has a weight that is, effectively, about 15 pounds for every square inch of Earth's surface. The average density of air at the Earth's surface is about 1.275 kg/m3. If the atmosphere were uniformly dense (it is not-the density varies quite significantly with altitude), how thick
A position vector has a length of 40.0 m and is at an angle of 57.0° above the x-axis. Find the vector's components.
In the triangle shown in the figure, the side lengths are a = 6.6 cm, b= 13.7 cm, and c = 9.2 cm. What is the value of the angle Î³ (See Appendix A for the law of cosines.)
Find the components of the vectors A, B, C, and D, if their lengths are given by A = 75.0, B = 60.0, C=25.0, D = 90.0 and their direction angles are as shown in the figure. Write the vectors in terms of unit vectors.
Use the components of the vectors from Problem 1.67 to finda) The sum A + B + C + D in terms of its componentsb) The magnitude and direction of the sum A-B + D
The Bonneville Salt Flats, located in Utah near the border with Nevada, not far from Interstate 180, cover an area of over 30,000 acres. A race car driver on the Flats first heads north for 4.47 km, then makes a sharp turn and heads southwest for 2.49 km, then makes another turn and heads east for
A map in a pirate's log gives directions to the location of a buried treasure. The starting location is an old oak tree. According to the map, the treasure's location is found by proceeding 20 paces north from the oak tree and then 30 paces northwest. At this location, an iron pin is sunk in the
The next page of the pirate's log contains a set of directions that differ from those on the map in Problem 1.70. These say the treasure's location is found by proceeding 20 paces north from the old oak tree and then 30 paces northwest. After finding the iron pin, one should "walk 12 paces nor'ward
The Earth's orbit has a radius of 1.5-10 m, and that of Venus has a radius of 1.1 ∙ 1011 m. Consider these two orbits to be perfect circles (though in reality they are ellipses with slight eccentricity). Write the direction and length of a vector from Earth to Venus (take the direction from Earth
A friend walks away from you a distance of 550 m, and then turns (as if on a dime) an unknown angle, and walks an additional 178 m in the new direction. You use a laser range-finder to find out that his final distance from you is 432 m. What is the angle between his initial departure direction and
Estimate the product of 4,308,229 and 44 to one significant figure (show your work and do not use a calculator), and express the result in standard scientific notation.
Find the vector C that satisfies the equation
A position vector has components x-34.6 m and y = -53.5 m. Find the vectors length and angle with the x-axis.
For the planet Mars, calculate the distance around the Equator, the surface area, and the volume. The radius of Mars is 3.39∙106 m.
Find the magnitude and direction of (a) 9B - 3A and (b) -5A + 8B, where A = (23.0,59.0), B = (90.0,-150.0).
Express the vectors A = (Ax, Ay) = (-30.0 m,-50.0 m) and B = (Bx, By) = (30.0 m, 50.0 m) by giving their magnitude and direction as measured from the positive x-axis.
The force F that a spring exerts on you is directly proportional to the distance x that you stretch it beyond its resting length. Suppose that when you stretch a spring 8.00 cm, it exerts a force of 200. N on you. How much force will it exert on you if you stretch it 40.0 cm?
The distance a freely falling object drops, starting from rest, is proportional to the square of the time it has been falling. By what factor will the distance fallen change if the time of falling is three times as long?
A pilot decides to take his small plane for a Sunday afternoon excursion. He first flies north for 155.3 miles, then makes a 90° turn to his right and flies on a straight line for 62.5 miles, then makes another 90° turn to his right and flies 47.5 miles on a straight line.a) How far away from his
As the photo shows, during a total eclipse, the Sun and the Moon appear to the observer to be almost exactly the same size. The radii of the Sun and Moon are rs = 6.96ˆ™108 m and rM = 1.74ˆ™106 m, respectively. The distance between the Earth and the Moon is dEM = 3.84ˆ™108 m. Total solar
A hiker travels 1.50 km north and turns to a heading of 20.0° north of west, traveling another 1.50 km along that heading. Subsequently, she then turns north again and travels another 1.50 km. How far is she from her original point of departure, and what is the heading relative to that initial
Assuming that 1 mole (6.02 ∙ 1023 molecules) of an ideal gas has a volume of 22.4 L at standard temperature and pressure (STP) and that nitrogen, which makes up 78% of the air we breathe, is an ideal gas, how many nitrogen molecules are there in an average 0.5-1. breath at STP?
On August 27, 2003, Mars approached as close to Earth as it will for over 50,000 years. If its angular size (the planet's diameter, measured by the angle the radius subtends) on that day was measured by an astronomer to be 24.9 seconds of arc, and its diameter is known to be 6784 km, how close was
A football field's length is exactly 100 yards, and its width is 53 1/3 yards. A quarterback stands at the exact center of the field and throws a pass to a receiver standing at one corner of the field. Let the origin of coordinates be at the center of the football field and the x-axis point along
The circumference of the Cornell Electron Storage Ring is 768.4 m. Express the diameter in inches, to the proper number of significant figures.
1. The resultant of the two-dimensional vectors (1.5 m, 0.7 m), (-3.2 m, 1.7 m), and (1.2 m, -3.3 m) lies in quadrant __________.a) Ib) IIc) IIId) IV2. By how much does the volume of a cylinder change if the radius is halved and the height is doubled?a) The volume is quartered.b) The volume is cut
Roughly 4% to 5% of what you exhale is carbon dioxide. Assume that 22.4 L is the volume of 1 mole (6.02 ∙ 1023 molecules) of carbon dioxide and that you exhale 0.5 L per breath.a) Estimate how many carbon dioxide molecules you breathe out each day.b) If each mole of carbon dioxide has a mass of
The Earth's orbit has a radius of 1.5∙1011 m, and that of Mercury has a radius of 4.6 ∙ 1010 m. Consider these orbits to be perfect circles (though in reality they are ellipses with slight eccentricity). Write down the direction and length of a vector from Earth to Mercury (take the direction
The star (other than the Sun) that is closest to Earth is Proxima Centauri. Its distance from Earth can be measured using parallax. Parallax is half the apparent angular shift of the star when observed from Earth at points on opposite sides of the Sun. The parallax of Proxima Centauri is 769 milli
Write the vectors A, B, and C in Cartesian coordinates.
Calculate the length and direction of the vectors A, B, and C.
Add the three vectors A, B, and C graphically.
Determine the difference vector E = B - A graphically.
Add the three vectors A, B, and C using the component method, and find their sum vector D.
Use the component method to determine the length of the vector F = C - A - B.
Sketch the vectors with the components A = (Ax, Ay) = (30.0 m, -50.0 m) and B = (Bx, By) = (-30.0 m, 50.0 m), and find the magnitudes of these vectors.
1. An arrow is shot horizontally with a speed of 20. m/s from the top of a tower 60. m high. The time to reach the ground will be a) 8.9 s. b) 7.1s. c) 3.5 s. d) 2.6 s. e) 1.0 s. 2. A projectile is launched from the top of a building with an initial velocity of 30.0 m/s at an angle of 60.0° above
For a Science Olympiad competition, a group of middle school students build a trebuchet that can fire a tennis ball from a height of 1.55 m with a velocity of 10.5 m/s and a launch angle of 35.0° above the horizontal. What is the x-component of the velocity of the tennis ball just before it hits
For a Science Olympiad competition, a group of middle school students build a trebuchet that can fire a tennis ball from a height of 1.55 m with a velocity of 10.5 m/s and a launch angle of 35.0° above the horizontal. What is the y-component of the velocity of the tennis ball just before it hits
For a Science Olympiad competition, a group of middle school students build a trebuchet that can fire a tennis ball from a height of 1.55 m with a velocity of 10.5 m/s and a launch angle of 35.0° above the horizontal. What is the speed of the tennis ball just before it hits the ground?
A pilot flies her airplane from its initial position to a position 200.0 km north of that spot. The airplane flies with a speed of 250.0 km/h with respect to the air. The wind is blowing west to east with a speed of 45.0 km/h. In what direction should the pilot steer her plane to accomplish this
A pilot flies her airplane from its initial position to a position 200.0 km north of that spot. The airplane flies with a speed of 250.0 km/h with respect to the air. The wind is blowing west to east with a speed of 45.0 km/h. What is the speed of the plane with respect to the ground?
A pilot flies her airplane from its initial position to a position 200.0 km north of that spot. The airplane flies with a speed of 250.0 km/h with respect to the air. The wind is blowing west to east with a speed of 45.0 km/h. How long will it take to make the trip?
A ball is thrown from ground at an angle between 0° and 90°. Which of the following remain constant: x, y, vx, vy, ay?
A ball is thrown straight up by a passenger in a train that is moving with a constant velocity. Where would the ball land-back in his hands, in front of him, or behind him? Does your answer change if the train is accelerating in the forward direction? If yes, how?
A rock is thrown at an angle 45° below the horizontal from the top of a building. Immediately after release will its acceleration be greater than, equal to, or less than the acceleration due to gravity?
Three halls of different masses are thrown horizontally from the same height with different initial speeds, as shown in the figure. Rank in order, from the shortest to the longest, the times the halls take to hit the ground.
5. A 50-g ball rolls off a countertop and lands 2 m from the base of the counter. A 100-g ball rolls off the same countertop with the same speed. It lands from the base of the counter. a) Less than 1 m b) 1 m c) 2m d) 4 m e) more than 4 m 6. For a given initial speed of an ideal projectile, there
To attain maximum height for the trajectory of a projectile, what angle would you choose between 0° and 90°, assuming that you can launch the projectile with the same initial speed independent of the launch angle. Explain your reasoning.
An airplane is traveling at a constant horizontal speed v, at an altitude h above a lake, when a trapdoor at the bottom of the airplane opens and a package is released (falls) from the plane. The airplane continues horizontally at the same altitude and velocity. Neglect air resistance. a) What is
Two cannonballs are shot in sequence from a cannon, into the air, with the same muzzle velocity, at the same launch angle, based on their trajectory and range, how can you tell which one is made of wood and which one is made of wood. If the same cannonballs were launched in vacuum, what would your
One should never jump off a moving vehicle (train, car, bus, etc.). Assuming, however, that one does perform such a jump, from a physics standpoint, what would be the best direction to jump in order to minimize the impact of the landing? Explain.
A boat travels at a speed of vBW relative to the water in a river of width D. The speed at which the water is flowing is vw.a) Prove that the time required to cross the river to a point exactly opposite the starting point and then to return isb) Prove that the time for the boat to travel a distance
A rocket-powered hockey puck is moving on a (frictionless) horizontal air-hockey table. The A- and/-components of its velocity as a function of time are presented in the graphs below. Assuming that at t = 0 the puck is at (x0, y0) = (1, 2), draw a detailed graph of the trajectory y(x).
For a certain object in three-dimensional motion, the x-, y-, and z-coordinates as a function of time are given byDescribe the motion and the trajectory of the object in an xyz coordinate system.
An object moves in the x and y-coordinates of the object as a function of time are given by the following equations: x(f) = 4.9t2 + 2t + 1 and y(t) = 3t + 2. What is the velocity vector of the object as a function of time? What is its acceleration vector at the time t = 2 s?
A particle's motion is described by the following two parametric equations: x(t) = 5cos(2πt) y(t) = 5sin(2πt) where the displacements are in meters and t is the time, in seconds. a) Draw a graph of the particle's trajectory (that is, a graph of y versus x). b) Determine the equations that
In a proof-of-concept experiment for an antiballistic missile defense system, a missile is (i red from the ground of a shooting range toward a stationary target on the ground. The system detects the missile by radar, analyzes in real time its parabolic motion, and determines that it was fired from
9. The acceleration due to gravity on the Moon is 1.62 m/s2, approximately a sixth of the value on Earth. For a given initial velocity v0 and a given launch angle θa, the ratio of the range of an ideal projectile on the Moon to the range of the same projectile on Earth, RMoon / REarth, will be
A projectile is launched at an angle of 45.0° above the horizontal. What is the ratio of its horizontal range to its maximum height? How does the answer change if the initial speed of the projectile is doubled?
In a projectile motion, the horizontal range and the maximum height attained by the projectile are equal.a) What is the launch angle?b) if everything else stays the same, how should the launch angle, θ0, of the projectile be changed for the range to be halved?
An air-hockey puck has a model rocket rigidly attached to it. The puck is pushed from one corner along the long side of the 2.00-m-long air-hockey table, with the rocket pointing along the short side of the table, and at the same time the rocket is fired. If the rocket thrust imparts an
On a battlefield, a cannon fires a cannonball up a slope, from ground level, with an initial velocity v0 at an angle θ0 above the horizontal. The ground itself makes an angle a above the horizontal (α < θ0). What is the range R of the cannonball, measured along the inclined ground? Compare your
Two swimmers with a soft spot for physics engage in a peculiar race that models a famous optics experiment: the Michelson-Morley experiment. The race takes place in a river 50.0 m wide that is flowing at a steady rate of 3.00 in/s. Both swimmers start at the same point on one bank and swim at the
What is the magnitude of an objects average velocity if the object moves from a point with coordinates x = 2.0 m, y = -3.0 m to a point with coordinates x = 5.0 m, y = -9.0 m in a time interval of 2.4 s?
A man in search of his dog drives first 10.0 mi northeast, then 12.0 mi straight south, and finally 8.0 mi in a direction 30.0° north of west. What are the magnitude and direction of his resultant displacement?
During a jaunt on your sailboat, you sail 2.00 km east, then 4.00 km southeast, and finally an additional distance in an unknown direction. Your final position is 6.00 km directly east of the starting point. Find the magnitude and direction of the third leg of your journey.
A truck travels 3.02 km north and then makes a 90.0° left turn and drives another 4.30 km. The whole trip takes 5.00 min. a) With respect to a two-dimensional coordinate system on the surface of Earth such that the y-axis points north, what is the net displacement vector of the truck for this
A rabbit runs in a garden such that the x- and y-components of its displacement as functions of time are given by x(t) = -0.45t2 - 6.5t + 25 and y(t) = 0.35t2 + 8.3f + 34. (Both x and y are in meters and t is in seconds.)a) Calculate the rabbits position (magnitude and direction) at t = 10.0 s.b)
Some rental cars have a GPS unit installed, which allows the rental car company to check where you are at all times and thus also know your speed at any time. One of these rental cars is driven by an employee in the company's lot and, during the time interval from 0 to 10.0 s, is found to have a
A skier launches off a ski jump with a horizontal velocity of 30.0 m/s (and no vertical velocity component). What are the magnitudes of the horizontal and vertical components of her velocity the instant before she lands 2.00 s later?
An archer shoots an arrow from a height of 1.14 m above ground with an initial speed of 47.5 m/s and a launch angle of 35.2° above the horizontal. At what time after the release of the arrow from the bow will the arrow be flying exactly horizontally?
A football is punted with an initial speed of 27.5 m/s and a launch angle of 56.7°. What is its hang time (the time until it hits the ground again)?
You serve a tennis ball from a height of 1.80 m above the ground. The ball leaves your racket with a speed of 18.0 m/s at an angle of 7.00° above the horizontal. The horizontal distance from the court's baseline to the net is 11.83 m, and the net is 1.07 m high. Neglect any spin imparted on the
Stones are thrown horizontally with the same velocity from two buildings. One stone lands twice as far away from its building as the other stone. Determine the ratio of the heights of the two buildings.
You are practicing throwing darts in your dorm. You stand 3.00 m from the wall on which the board hangs. the dart leaves your hand with a horizontal velocity at a point 2.00 m above the ground. the dart strikes the board at a point 1.65 m from the ground. Calculate:a) The time of flight of the
A football player kicks a ball with a speed of 22.4 m/s at an angle of 49.0° above the horizontal from a distance of 39.0 m from the goalpost.a) By how much does the ball clear or fall short of clearing the crossbar of the goalpost if that bar is 3.05 m high?b) What is the vertical velocity of the
An object fired at an angle of 35.0° above the horizontal takes 1.50 s to travel the last 15.0 m of its vertical distance and the last 10.0 m of its horizontal distance. With what speed was the object launched? (Note: The problem does not specify that the initial and final elevation of the object
A conveyor belt is used to move sand from one place to another in a factory. The conveyor is tilted at an angle of 14.0° above the horizontal and the sand is moved without slipping at the rate of 7.00 m/s. The sand is collected in a big drum 3.00 m below the end of the conveyor belt. Determine the
Your friend's car is parked on a cliff overlooking the ocean on an incline that makes an angle of 17.0° below the horizontal. The brakes fail, and the car rolls from rest down the incline for a distance of 29.0 m to the edge of the cliff, which is 55.0 m above the ocean, and, unfortunately,
An object is launched at a speed of 20.0 m/s from the top of a tall tower. The height y of the object as a function of the time f elapsed from launch is y(f) = -4.90f2 + 19.32/ + 60.0, where h is in meters and t is in seconds. Determine: a) The height H of the tower; b) The launch angle; c) The
A projectile is launched at a 60.0° angle above the horizontal on level ground. The change in its velocity between launch and just before landing is found to beWhat is the initial velocity of the projectile? What is its final velocity just before landing?
The figure shows the paths of a tennis ball your friend drops from the window of her apartment and of the rock you throw from the ground at the same instant. The rock and the ball collide at x = 50.0 m, y = 10.0 m and r n 3.00 s. If the ball was dropped from a height of 54.1 m, determine the
For a science fair competition, a group of high school students build a kicker-machine that can launch a golf ball from the origin with a velocity of 11.2 m/s and a launch angle of 31.5° with respect to the horizontal.a) Where will the golf ball fall back to the ground?b) How high will it be at

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