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college physics reasoning

College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions

Draw a graph showing the position x as a function of time for an object whose acceleration is (a) Constant and positive, (b) Constant and negative, and (c) Positive and increasing with time. Assume the object starts at x = 0 in parts (a) and (c) and at a positive value of x in
A car travels along a straight, level road. The car begins a distance x - 25 m from the origin at t - 0.0 s. At t - 5.0 s, the car is at x - 100 m; at t - 8.0 s, it is at x - 300 m. Find the average velocity of the car during the interval from t - 0.0 s to t - 5.0 s and during the interval from t -
A squirrel falls from a very tall tree. Initially (at t = 0), the squirrel is at the top of the tree, a distance y = 50 m above the ground. At t - 1.0 s, the squirrel is at y - 45 m, and at t - 2.0 s it is at y - 30 m. Estimate the average velocity of the squirrel during the intervals from t - 0.0
A spacecraft takes off from Cape Canaveral in Florida and orbits Earth 18 times before landing back at Cape Canaveral 24 hours and 15 minutes later. During this time, it moves in a circular orbit with radius 6.7 × 106 m. (a) What is the average speed of the space shuttle during its
Figure P2.35 shows the velocity as a function of time for an object. (a) What is the average acceleration during the interval from t = 0 s to t = 20 s? (b) Estimate the instantaneous acceleration at t - 5 s, (c) At t - 10 s, and (d) At t - 20 s.Figure P2.35 v (m/s) |20아 10+ t
Figure P2.36 shows the acceleration as a function of time for an object. (a) If the object starts from rest at t - 0, what is the velocity of the object as a function of time? (b) If the object instead has a velocity of +40 m/s at t = 0, how does your result for part (a) change?Figure
A rabbit runs in a straight line with a velocity of +1.5 m/s for a period of time, rests for 10 s, and then runs again along the same line at +0.60 m/s for an unknown amount of time. The rabbit travels a total distance of 1200 m, and its average speed is 0.80 m/s. (a) What is the total time
Figure 2.24 (page 39) shows one of Galileo€™s experiments in which a ball rolls up an incline. A ball that is initially rolling up the incline will roll up to some maximum height and then roll back down the incline. Draw qualitative plots of the position and velocity as functions of time
A block is sliding at a particular initial speed v when it encounters the following horizontal surfaces: (a) A grass field, (b) An asphalt street, (c) A hardwood floor, (d) An ice rink (with real, not ideal, ice), and (e) An ideal, friction less surface. Draw qualitative
An unsafe way to transport your penguin. A flatbed truck hauls a block of ice on top of which stands a penguin (see Fig. P2.40). Assume the block of ice is frozen solid to the bed of the truck, but the top surface of the ice is extremely slippery. The truck skids to a stop from an initial velocity
A flatbed rail car is moving at a slow but constant velocity. A man stands in the rail car, facing sideways (perpendicular) to the motion of the rail car. The man holds a baseball at arm’s length and drops it onto the rail car bed. Where does the principle of inertia predict that the ball will
The person shown in Figure 2.1 (page 27) is pushing on a refrigerator that sits on a level floor. Assume the section of the floor underneath the refrigerator is very slippery so that the only horizontal force on the refrigerator is due to the person. If the force exerted by the person has a
Action and reaction. Consider again the man pushing the refrigerator in Problem 42, but now assume the entire floor, including the portion under the man, is friction less. Use Newton€™s third law along with his second law to find the acceleration of the man. Assume he has a mass of 60
In SI units, force is measured in newtons, with 1 N = 1 kg • m/s2. Which of the following combinations of units can also be used to measure force?(a) g • m/s(b) g • cm2/s(c) kg • m4/(s2 cm3)(d) g • cm/s2(e) kg • miles/(minutes)2
In the U.S. customary system of units, mass is measured in units called slugs. Suppose an object has a mass of 15 kg. Use the conversion factors inside the front cover of this book to express the mass of the object in slugs.
In the U.S. customary system of units, force is measured in units of pounds (abbreviated lb). Suppose the force on an object is 150 lb. Using the conversion factors inside the front cover of this book, express this force in units of newtons.
A force is found to be 240 g • cm/s2. Convert this value into units of newtons.
A cannon is fired horizontally from a platform (Fig. P2.49). The platform rests on a flat, icy, friction less surface. Just after the shell is fired and while it is moving through the barrel of the gun, the shell (mass 3.2 kg) has an acceleration of +2500 m/s2. At the same time, the cannon has an
According to Newton’s third law, for every force there is always a reaction force of equal magnitude and opposite direction. In each of the examples below, identify an action–reaction pair of forces.(a) A tennis racket hits a tennis ball, exerting a force on the ball.(b) Two ice skaters are
Tom has two ways he could drive home from work. He could take Highway 99 for 45 miles with a speed limit of 65 mi/h, or he could take Interstate 5, which would take him a bit out of the way at 57 miles, but with a speed limit of 75 mi/h. (a) Assuming Tom misses the rush hour and drives at an
Throwing heat. In professional baseball, most pitchers can throw a fastball at a speed of 90 mi/h. For simplicity, assume the pitcher releases the ball just above the center of the pitcher’s mound. (a) Given that the regulation distance from the pitcher’s mound to home plate is 60.5 ft,
Figure P2.53 shows the position as a function of time for an object. (a) What is the average velocity during the period from t = 0.0 s to t = 10.0 s? (b) What is the average velocity between t = 0.0 s and t = 5.0 s? (c) Between t = 5.0 s and t = 10.0 s? (d) Explain why and how
Figure P2.55 shows the position as a function of time for an apple that falls from a very tall tree.? (a) At what time does the apple hit the ground?? (b) Use a graphical approach to estimate and plot the acceleration as a function of time.? (c) Make a sketch of the velocity of the apple as a
Identify an action–reaction pair of forces in each of the following situations.(a) A person pushing on a wall(b) A book resting on a table(c) A hockey puck sliding across an icy surface(d) A car accelerating from rest(e) An object undergoing free fall in a vacuum(f) A basketball player jumping to
A cheetah runs a distance of 100 m at a speed of 25 m/s and then runs another 100 m in the same direction at a speed of 35 m/s. What is the cheetah’s average speed? Explain why the correct answer is not just the average of the speeds during the first and last 100 m.
Astronaut frequent-flyer miles. The average speed of a spacecraft while in orbit is about 8900 m/s. How far does the spacecraft travel during a mission that lasts 7.5 days?
A cat is being chased by a dog. Both are running in a straight line at constant speeds. The cat has a head start of 3.5 m. The dog is running with a speed of 8.5 m/s and catches the cat after 6.5 s. How fast did the cat run?
Predator and prey. The author???s cat enjoys chasing chipmunks in the front yard. In this game, the cat sits at one edge of a yard that is w - 30 m across (Fig. P2.59), watching as chipmunks move toward the center. The cat can run faster than a chipmunk, and when a chipmunk moves more than a
A thief is trying to escape from a parking garage after completing a robbery, and the thief???s car is speeding (v = 12 m/s) toward the door of the parking garage (Fig. P2.60). When the thief is L - 30 m from the door, a police officer flips a switch to close the garage door. The door starts at a
The radius of Jupiter is 11 times as large as the radius of Earth. What is the ratio of the volume of Jupiter to the volume of Earth?
Consider the following three vectors, described here by their lengths and angles with respect to the x axis: A(vector): 5.0 cm, 30º; B(vector): 7.5 cm, 0º; and C(vector): 10.0 cm, 350º. (a) Using the tip-to-tail graphical method for vector addition, show that the order in which these
The unit of area called the acre comes from an old system of measurement in which 1 acre is the area of a rectangle whose length is 220 yards and whose width is 22 yards. (a) Determine the number of acres in 1 square mile. (b) How many square meters are in 1 acre? (c) How many square
Find the components of the vector C(vector) in parts (a) through (d) of Problem 56.Data From Problem 56A vector A(vector) has a magnitude of 15 (in some unspecified units) and makes an angle of 25º with the x axis, and a vector B(vector) has a magnitude of 25 and make an angle of 70º with the x
Consider the equations5x + 2y - 13 -3x + 7y 5- 25(a) Put each equation into the standard format for a straight line (y = mx + b) and plot both lines. Use your graph to find the point (x, y) where these lines intersect. (b) Use algebra to find the values of x and y
Which vector in Figure P1.51 might equal A(vector) + B(vector)? Figure P1.51 ? (a) (b) Á -B (c) (d)
A vector has components Ax = 54 m and Ay = 23 m. Find the length of the vector A(vector) and the angle it makes with the x axis.
A ladder of length 2.5 m is leaned against a wall (Fig. P1.44). If the top of the ladder is 1.7 m above the floor, what is the angle the ladder makes with the wall? What angle does it make with the floor? Figure P1.44 ? L = 2.5 m
The car in Figure P1.42 travels a distance of 750 m along the track, and the driver finds that she has traveled through an angle of 450º. What is the radius of the track? Figure P1.42 y
A car travels on a circular track (Fig. P1.42) of radius r = 38 m. If the car travels a distance of 210 m along the track, through what angle (in rad) does the car move? Figure P1.42 y
The thickness of a typical piece of paper is 6 × 10–5 m. Suppose a large stack of papers is assembled, reaching to the top floor of the Empire State Building. Approximately how many pieces of paper are in the stack?
Steep grade. A mountain road makes an angle θ = 8.5º with the horizontal direction (Fig. P1.45). If the road has a total length of 3.5 km, how much does it climb? That is, find h. Figure P1.45 ? h
Consider the vectors A(vector) and B(vector) in Figure P1.46.? (a) Draw a picture that graphically constructs the sum of these two vectors A(vector) + B(vector) (i.e., similar to what was done in Fig. 1.12). Also construct A(vector) - B(vector), B(vector) - A(vector), A(vector) - 5B(vector), and
A vector of length of 2.5 m makes an angle of 38º with the y axis. Find the components of the vector.
Which of the vectors in Figure P1.49 have approximately the same magnitude? Figure P1.49 ? (a). L(b)시 (c)_ (d). (e) (f) (g) (h)
Which of the vectors in Figure P1.49 have approximately the same direction? Figure P1.49 ? (a). L(b)시 (c)_ (d). (e) (f) (g) (h)
A vector in x-y plane has a length of 4.5 m and y-component of -2.7m. What angle does this vector make with the X-axis? Why does this problem have two answers?
Consider a map oriented so that the x axis runs east–west (with east being the “positive” direction) and y runs north–south (with north “positive”). A person drives 15 km to the west and then turns and drives 45 km to the south. Find the magnitude and direction of the total movement of
Consider a map oriented so that the x axis runs east–west (with east being the “positive” direction) and y runs north–south (with north “positive”). A person drives 25 km to the north, turns and drives 75 km to the east, and then turns north and drives for an unknown distance z. If his
Consider the vector C(Vector) in Figure P1.55. Construct a drawing that shows the vector C(Vector) along with the vector 4C(Vector), - C(Vector), and - 3C(Vector). Figure P1.55 y
A vector A(vector) has a magnitude of 15 (in some unspecified units) and makes an angle of 25º with the x axis, and a vector B(vector) has a magnitude of 25 and make an angle of 70º with the x axis. Compute the magnitudes and directions of the vector:(a) C(vector) - A(vector) + B(vector)(b)
A boater travels from some initial point P1?to a final point P2along the dashed line shown in Figure P1.58. Find θ and the total distance traveled. Figure P1.58 ? y P -77 m- 195 m P2
A car starts from the origin and is driven 1.2 km south and then 3.1 km in a direction 53º north of east. Relative to the origin, what is the car’s final location? Express your answer in terms of a distance and an angle.
A mountaineer uses a global positioning system receiver to measure his displacement from base camp to the top of Mount McKinley. The coordinates of base camp are x = 0, y = 0, and z = 4300 m (here z denotes altitude), and those of the top of Mount McKinley are x = 1600 m, y = 4200 m, and z = 6200
Estimate the number of times a student’s heart will beat during the 4 years she is a college student.
The solar system in perspective. The diameters of the Earth and the Sun are approximately 1.3 × 107 m and 1.4 × 109 m respectively, and the average Sun–Earth distance is 1.5 × 1011 m. Consider a scale model of the solar system, where the Earth is represented by a peppercorn 3.7 mm in
A typical human baby at birth is about 20 inches as measured from head to toe. An adult is much longer. What is the approximate ratio of the height of an adult female to the length of a baby at birth?
You wish to replace the flooring in your kitchen with square linoleum tiles that measure 12 inches on a side. If your kitchen has a floor area of 10.7 square yards, how many such tiles will you need to buy?
A river flows with a current of 5.0 mi/h directly south. A small boat has a maximum speed in still water (i.e., on a quiet lake) of 10 mi/h. The pilot points the boat due east and sets the engine at full throttle to move the boat at maximum speed. In what direction does the boat actually move?
Approximately how many cells are there in the human body?
Approximately how fast does human hair grow? Express your answer in m/s.
At room temperature, 1.0 g of water has a volume of 1.0 cm3. (a) What is the approximate volume of one water molecule? (b) The human body is composed mainly of water. Assuming for simplicity your body is only water (and nothing else), find the approximate number of water molecules in your
A person stretches a rope of length 55 m between the top of a building to the base of a tree 25 m away (Fig. P1.71). How tall is the building? Figure P1.71 ? -Rope +25 m→|
If Saturn could fit in a bathtub, would it float? Use the planetary data in Appendix A to calculate the density (mass/volume) of Earth, Mars, Jupiter, and Saturn. What are the differences? Can you explain them? If an object has a density less than 1000 kg/m3, it will float in water. Would any of
Two vectors have lengths A = |A(vector)| = 12 m and B - |B(vector)| - 17 m, but their directions are unknown. (a) What are the maximum and minimum possible values of A(vector) + B(vector)? (b) What are the maximum and minimum values of A(vector) - B(vector)?
You are on a road trip, traveling by expressway from one city to another, without stopping and without leaving the expressway. If you obey the speed limit, approximately how far do you travel in 30 minutes? Express your answer in miles and in kilometers.
An angle has a value of 1.25 radians. Find its value in degrees.
An angle has a value of 738. Find its value in radians.
Find values of x, y, and r in Figure 1.8 that will give a right triangle in which one of the triangle???s interior angles is 0.70 radian. Figure 1.8 ? x2 + y2 = r2 y Right angle = 90°
A right triangle has an interior angle of 25º. What are the values of the other interior angle (the one besides the right angle)?
A right triangle (Fig. 1.8) has sides of length x = 4.5 m and y = 3.7 m.? (a) Find the value of r (the length of the hypotenuse).? (b) Find the values of the interior angles. Express your answers in degrees and radians.? (c) Find the sine, cosine, and tangent of the smaller interior angle.? (d)
Consider the motion of the hour hand of a clock. What angle does the hour hand make with respect to the vertical 12 o’clock position when it is (a) 3:00, (b) 6:00, (c) 6:30, (d) 9:00, and (e) 11:10? Express each angle in both degrees and radians, and measure angles
Two well-known organic chemicals are benzene, C6H6, and propane, C3H8. Benzene has a molecular weight of 78.11 g/mol and propane 44.096 g/mol, where the molecular weight is a useful measure in chemistry and is defined as the mass of 1 mole (Avogadro’s number) of molecules or atoms. Determine the
The speed v of a bullet satisfies the relation vt = 95 m, where t = 0.25 s. Find v.
Consider the equation 5x – 17 = 10x – 27. Solve for x.
The variable m has dimensions of mass, h and y have dimensions of length, and t has dimensions of time. What are the dimensions of the following quantities? (a) my/t, (b) hy/t2, (c) y3/(ht)
Consider the equation mgh -1/2mv2, where m has units of mass (kilograms), g has units of length/time2 (m/s2), h has units of length (meters), and v has units of length/time (m/s). (a) Is this equation dimensionally correct or incorrect? (b) Is the equation v2/h = g dimensionally correct
Sports cars. A Corvette C4 (circa 1971) came equipped with a huge 454 V8 engine, where the volume of the combustion chambers summed to 454 cubic inches (in.3). In modern engines, this volume is measured in SI units. For example, a 2005 Corvette Z06 touts a 7.0-liter V8 engine. Which engine has the
It takes about 190 s for light to travel from the Sun to the planet Mercury (the planet closest to the Sun) and about 15,000 s for light to travel from the Sun to Neptune (the farthest planet). Suppose it takes light 950 s to travel from the Sun to a particular asteroid. How many minutes does it
A cardboard box can hold exactly 1 cubic meter of volume (1 m3). Use the conversion factors 1 m = 100 cm = 1000 mm to find this volume expressed in units of (a) Cubic centimeters and (b) Cubic millimeters.
Michael Jordan is approximately 6.5 ft tall. What is his height in millimeters?
A bottle has a volume of 1.2 L. (a) What is its volume in cubic centimeters? (b) In cubic meters?
A card table has a top surface area of exactly 1 square meter (1 m2). What is its area as measured in (a) Square centimeters and (b) Square millimeters?
Express the distance from Chicago to New York City (Table 1.1, page 5) in (a) Miles, (b) Inches, (c) Kilometers, (d) Micrometers. TABLE 1.1 Some Common Lengths and Distances Length or Distance in Meters (m) Length or Distance in Meters (m) Quantity Quantity Diameter of a proton
Express 5.0 m in units of (a) Centimeters, (b) Feet, (c) Inches, (d) Miles.
An object has a mass of 273 g. What is its mass in kilograms?
Express 75 ft in units of (a) Meters and (b) Millimeters.
The age of the universe is about 5 Ã— 1017 s (Table 1.2, page 11). Express this age in years. TABLE 1.2 Some Common Time Intervals Time in Seconds (s) Quantity Time for light to travel 1 meter Time between heartbeats (approximate) 3.34 × 10-9 Time for light to travel from the Sun
A U.S. football field is 120 yards long (including the end zones). How long is the field in (a) Meters, (b) Millimeters, (c) Feet, and (d) Inches?
What is the volume of a basketball?
Calculate the volume of a typical 1000-page textbook. Express your answer in cubic meters (m3) and in cubic centimeters (cm3).
Write the following values using scientific notation. (a) The radius of the Earth, 6,370,000 m. (b) The distance from the Earth to the Moon, 384,000 km. (c) The mass of the Earth, 5,970,000,000,000,000,000,000,000 kg.
(a) Estimate the number of times your heart beats in 1 year. Express your answer in scientific notation. (b) Some people have (jokingly) suggested that each person has only a certain number of heartbeats before he or she dies. The average life expectancy for a person born in the United States
A hydrogen atom has a diameter of approximately 10–10 m. If this atom were expanded to the size of an apple, how big would a real apple be if it were expanded by the same amount? Can yous think of an object whose size is comparable to this gigantic apple?
For each of the following formulas and associated values, find and express the solution with the appropriate number of significant figures and units. (a) The area A of a rectangle of length L = 2.34 m and width w = 1.874 m. (b) The area A of a circle of radius r = 0.0034 m. (c) The
The speed of light is c = 299,792,458 m/s. (a) Write this value in scientific notation. (b) What is the value of c to four significant figures?
The magnitude of the momentum of an object is the product of its mass m and speed v. If m = 6.5 kg and v = 1.54 m/s, what is the magnitude of the momentum? Be sure to give the correct number of significant figures in your answer.
The mass of an object is m = 23 kg, and its volume is V = 0.005 m3. What is its density, m/V? Be sure to give the correct number of significant figures in your answer.
A football field in the United States is 120 yards long (including the end zones). With how many significant figures do you think this value should be written?
The distance from point B to point D in Figure P1.7 is 3.15 km while the distance from A to B is 3.45 km. What is the distance from A to D? Be sure to give the correct number of significant figures in your answer.Figure P1.7 D A B C
Astronomical distances. Spiral galaxies like our own Milky Way measure approximately 2 × 105 light-years in diameter, where 1 light-year (ly) equals the distance traveled by light in 1 year. Our nearest-neighbor galaxy is the great spiral galaxy Andromeda, which has been determined to be

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