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physics
college physics 2nd
College Physics 2nd Edition OpenStax - Solutions
At takeoff, a commercial jet has a 60.0 m/s speed. Its tires have a diameter of 0.850 m.(a) At how many rev/min are the tires rotating?(b) What is the centripetal acceleration at the edge of the tire?(c) With what force must a determined 1.00 × 10-15 kg bacterium cling to the rim?(d) Take the
Draw a free body diagram for a satellite in an elliptical orbit showing why its speed increases as it approaches its parent body and decreases as it moves away.
A large household air conditioner may consume 15.0 kW of power. What is the cost of operating this air conditioner 3.00 h per day for 30.0 d if the cost of electricity is $0.110 per kW.h?
Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Serving at a speed of 170 km/h, a tennis player hits the ball at a height of 2.5 m and an angle θ below the horizontal. The base line is 11.9 m from the net, which is 0.91 m high. What is the angle θ such that the ball just crosses the net? Will the ball land in the service box, whose service
An owl is carrying a mouse to the chicks in its nest. Its position at that time is 4.00 m west and 12.0 m above the center of the 30.0 cm diameter nest. The owl is flying east at 3.50 m/s at an angle 30.0º below the horizontal when it accidentally drops the mouse. Is the owl lucky enough to have
Suppose a soccer player kicks the ball from a distance 30 m toward the goal. Find the initial speed of the ball if it just passes over the goal, 2.4 m above the ground, given the initial direction to be 40° above the horizontal.
Can a goalkeeper at her/ his goal kick a soccer ball into the opponent’s goal without the ball touching the ground? The distance will be about 95 m. A goalkeeper can give the ball a speed of 30 m/s.
The free throw line in basketball is 4.57 m (15 ft) from the basket, which is 3.05 m (10 ft) above the floor. A player standing on the free throw line throws the ball with an initial speed of 8.15 m/s, releasing it at a height of 2.44 m (8 ft) above the floor. At what angle above the horizontal
In 2007, Michael Carter (U.S.) set a world record in the shot put with a throw of 24.77 m. What was the initial speed of the shot if he released it at a height of 2.10 m and threw it at an angle of 38.0° above the horizontal? (Although the maximum distance for a projectile on level ground is
A football player punts the ball at a 45.0° angle. Without an effect from the wind, the ball would travel 60.0 m horizontally. (a) What is the initial speed of the ball?(b) When the ball is near its maximum height it experiences a brief gust of wind that reduces its horizontal velocity by 1.50
Derivefor the range of a projectile on level ground by finding the time at which becomes zero and substituting this value of into the expression fornoting that R = la 2 sin 200 8
Prove that the trajectory of a projectile is parabolic, having the form y = ax + bx2. To obtain this expression, solve the equation x = v0xt for t and substitute it into the expression for y=v0yt-(1/2)gt2 (These equations describe the x and y positions of a projectile that starts at the origin.)
Unreasonable Results (a) Find the maximum range of a super cannon that has a muzzle velocity of 4.0 km/s.(b) What is unreasonable about the range you found?(c) Is the premise unreasonable or is the available equation inapplicable? Explain your answer.(d) If such a muzzle velocity could be
Construct Your Own Problem Consider an airplane headed for a runway in a cross wind. Construct a problem in which you calculate the angle the airplane must fly relative to the air mass in order to have a velocity parallel to the runway. Among the things to consider are the direction of the runway,
(a) A jet airplane flying from Darwin, Australia, has an air speed of 260 m/s in a direction 5.0° south of west. It is in the jet stream, which is blowing at 35.0 m/s in a direction 15° south of east. What is the velocity of the airplane relative to the Earth?(b) Discuss whether your answers are
(a) Use the distance and velocity data in Figure 3.59 to find the rate of expansion as a function of distance.(b) If you extrapolate back in time, how long ago would all of the galaxies have been at approximately the same position? The two parts of this problem give you some idea of how the Hubble
A ship sets sail from Rotterdam, The Netherlands, heading due north at 7.00 m/s relative to the water. The local ocean current is 1.50 m/s in a direction 40.0° north of east. What is the velocity of the ship relative to the Earth?
Critical Thinking Two identical spring-loaded launchers are fixed to the end of a table. Launcher A is inclined 40° above the horizontal and launcher B is inclined 50° above the horizontal.(a) Which of these launchers will fire the ball the greatest vertical height above the launcher before it
A sandal is dropped from the top of a 15.0-m-high mast on a ship moving at 1.75 m/s due south. Calculate the velocity of the sandal when it hits the deck of the ship: (a) Relative to the ship and(b) Relative to a stationary observer on shore.(c) Discuss how the answers give a consistent result for
A football quarterback is moving straight backward at a speed of 2.00 m/s when he throws a pass to a player 18.0 m straight downfield. The ball is thrown at an angle of 25° relative to the ground and is caught at the same height as it is released. What is the initial velocity of the ball relative
Which has more mass: a kilogram of cotton balls or a kilogram of gold?
The great astronomer Edwin Hubble discovered that all distant galaxies are receding from our Milky Way Galaxy with velocities proportional to their distances. It appears to an observer on the Earth that we are at the center of an expanding universe. Figure 3.59 illustrates this for five galaxies
An ice hockey player is moving at 8.00 m/s when they hit the puck toward the goal. The speed of the puck relative to the player is 29.0 m/s. The line between the center of the goal and the player makes a 90.0° angle relative to their path as shown in Figure 3.60. What angle must the puck's
Suppose that the net external force (push minus friction) exerted on a lawn mower is 51 N (about 11 lb) parallel to the ground. The mass of the mower is 24 kg. What is its acceleration?StrategySince Fnet and m are given, the acceleration can be calculated directly from Newton's second law as stated
(a) In what direction would the ship in Exercise 3.57 have to travel in order to have a velocity straight north relative to the Earth, assuming its speed relative to the water remains 7.00 m/s?(b) What would its speed be relative to the Earth?
An athlete crosses a 25-m-wide river by swimming perpendicular to the water current at a speed of 0.5 m/s relative to the water. They reach the opposite side at a distance 40 m downstream from the starting point. How fast is the water in the river flowing with respect to the ground? What is the
(a) Another airplane is flying in a jet stream that is blowing at 45.0 m/s in a direction 20° south of east (as in Exercise 3.58). Its direction of motion relative to the Earth is 45.0° south of west, while its direction of travel relative to the air is 5.00° south of west. What is the
Unreasonable Results A commercial airplane has an air speed of 280 m/s due east and flies with a strong tailwind. It travels 3000 km in a direction 5° south of east in 1.50 h.(a) What was the velocity of the plane relative to the ground?(b) Calculate the magnitude and direction of the tailwind's
What properties do forces have that allow us to classify them as vectors?
A seagull flies at a velocity of 9.00 m/s straight into the wind.(a) If it takes the bird 20.0 min to travel 6.00 km relative to the Earth, what is the velocity of the wind?(b) If the bird turns around and flies with the wind, how long will he take to return 6.00 km?(c) Discuss how the wind affects
Bryan Allen pedaled a human-powered aircraft across the English Channel from the cliffs of Dover to Cap Gris-Nez on June 12, 1979. (a) He flew for 169 min at an average velocity of 3.53 m/s in a direction 45° south of east. What was his total displacement?(b) Allen encountered a headwind averaging
A 63.0-kg sprinter starts a race with an acceleration of 4.20 m/s2. What is the net external force on him?
Unreasonable Results Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth.(a) At what velocity must the supplies be launched? (b) What is unreasonable about this velocity?(c) Is there a problem with the relative velocity between the
Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Verify that the coin dropped by the airline passenger in the Example 3.8 travels 144 m horizontally while falling 1.50 m in the frame of reference of the Earth.Data given in Example 3.8An airline passenger drops a coin while the plane is moving at 260 m/s. What is the velocity of the coin when it
Bryan Allen pedaled a human-powered aircraft across the English Channel from the cliffs of Dover to Cap Gris-Nez on June 12, 1979. (a) He flew for 169 min at an average velocity of 3.53 m/s in a direction 45° south of east. What was his total displacement?(b) Allen encountered a headwind averaging
A seagull flies at a velocity of 9.00 m/s straight into the wind.(a) If it takes the bird 20.0 min to travel 6.00 km relative to the Earth, what is the velocity of the wind?(b) If the bird turns around and flies with the wind, how long will he take to return 6.00 km?(c) Discuss how the wind affects
Verify that the coin dropped by the airline passenger in the Example 3.8 travels 144 m horizontally while falling 1.50 m in the frame of reference of the Earth.Data given in Example 3.8An airline passenger drops a coin while the plane is moving at 260 m/s. What is the velocity of the coin when it
A football quarterback is moving straight backward at a speed of 2.00 m/s when he throws a pass to a player 18.0 m straight downfield. The ball is thrown at an angle of 25° relative to the ground and is caught at the same height as it is released. What is the initial velocity of the ball relative
A ship sets sail from Rotterdam, The Netherlands, heading due north at 7.00 m/s relative to the water. The local ocean current is 1.50 m/s in a direction 40.0° north of east. What is the velocity of the ship relative to the Earth?
(a) A jet airplane flying from Darwin, Australia, has an air speed of 260 m/s in a direction 5.0° south of west. It is in the jet stream, which is blowing at 35.0 m/s in a direction 15° south of east. What is the velocity of the airplane relative to the Earth?(b) Discuss whether your answers are
(a) In what direction would the ship in Exercise 3.57 have to travel in order to have a velocity straight north relative to the Earth, assuming its speed relative to the water remains 7.00 m/s?(b) What would its speed be relative to the Earth?
(a) Another airplane is flying in a jet stream that is blowing at 45.0 m/s in a direction 20° south of east (as in Exercise 3.58). Its direction of motion relative to the Earth is 45.0° south of west, while its direction of travel relative to the air is 5.00° south of west. What is the
The great astronomer Edwin Hubble discovered that all distant galaxies are receding from our Milky Way Galaxy with velocities proportional to their distances. It appears to an observer on the Earth that we are at the center of an expanding universe. Figure 3.59 illustrates this for five galaxies
A sandal is dropped from the top of a 15.0-m-high mast on a ship moving at 1.75 m/s due south. Calculate the velocity of the sandal when it hits the deck of the ship: (a) Relative to the ship and(b) Relative to a stationary observer on shore.(c) Discuss how the answers give a consistent result for
(a) Use the distance and velocity data in Figure 3.59 to find the rate of expansion as a function of distance.(b) If you extrapolate back in time, how long ago would all of the galaxies have been at approximately the same position? The two parts of this problem give you some idea of how the Hubble
An ice hockey player is moving at 8.00 m/s when they hit the puck toward the goal. The speed of the puck relative to the player is 29.0 m/s. The line between the center of the goal and the player makes a 90.0° angle relative to their path as shown in Figure 3.60. What angle must the puck's
An athlete crosses a 25-m-wide river by swimming perpendicular to the water current at a speed of 0.5 m/s relative to the water. They reach the opposite side at a distance 40 m downstream from the starting point. How fast is the water in the river flowing with respect to the ground? What is the
Unreasonable Results Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth.(a) At what velocity must the supplies be launched? (b) What is unreasonable about this velocity?(c) Is there a problem with the relative velocity between the
Unreasonable Results A commercial airplane has an air speed of 280 m/s due east and flies with a strong tailwind. It travels 3000 km in a direction 5° south of east in 1.50 h.(a) What was the velocity of the plane relative to the ground?(b) Calculate the magnitude and direction of the tailwind's
Construct Your Own Problem Consider an airplane headed for a runway in a cross wind. Construct a problem in which you calculate the angle the airplane must fly relative to the air mass in order to have a velocity parallel to the runway. Among the things to consider are the direction of the runway,
Critical Thinking Two identical spring-loaded launchers are fixed to the end of a table. Launcher A is inclined 40° above the horizontal and launcher B is inclined 50° above the horizontal.(a) Which of these launchers will fire the ball the greatest vertical height above the launcher before it
A 63.0-kg sprinter starts a race with an acceleration of 4.20 m/s2. What is the net external force on him?
Which has more mass: a kilogram of cotton balls or a kilogram of gold?
Suppose that the net external force (push minus friction) exerted on a lawn mower is 51 N (about 11 lb) parallel to the ground. The mass of the mower is 24 kg. What is its acceleration?StrategySince Fnet and m are given, the acceleration can be calculated directly from Newton's second law as stated
Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
What properties do forces have that allow us to classify them as vectors?
Prior to space flights carrying astronauts, rocket sleds were used to test aircraft, missile equipment, and physiological effects on human subjects at high speeds. They consisted of a platform that was mounted on one or two rails and propelled by several rockets. Calculate the magnitude of force
Show that 1.0 m/s = 3.6 km/h.
Dragsters can actually reach a top speed of 145m/s in only 4.45 s—considerably less time than given in Example 2.10 and Example 2.11.(a) Calculate the average acceleration for such a dragster.(b) Find the final velocity of this dragster starting from rest and accelerating at the rate found in (a)
Determine the number of significant figures in the following measurements:a. 0.0009b. 15,450.0c. 6 × 103d. 87.990e. 30.42
A dolphin in an aquatic show jumps straight up out of the water at a velocity of 13.0 m/s.(a) List the knowns in this problem.(b) How high does his body rise above the water? To solve this part, first note that the final velocity is now a known and identify its value. Then identify the unknown, and
Using approximate values, calculate the slope of the curve in Figure 2.60 to verify that the velocity at t = 30.0 s is approximately 0.24 m/s.Data given in Figure 2.60 Position (m) 25 20+ 15+ 10+ 5+ 0 Position vs. Time 10 20 30 40 50 Time (s) 60 70 80
A ball is thrown horizontally from the top of a 60.0-m building and lands 100.0 m from the base of the building. Ignore air resistance.(a) How long is the ball in the air?(b) What must have been the initial horizontal component of the velocity?(c) What is the vertical component of the velocity just
Verify the ranges for the projectiles in Figure 3.38(a) for θ = 45° and the given initial velocities.Data given in Figure 3.38 (a) (b) 50 m/s 40 m/s 30 m/s 45° R=91.8 m Vo = 50 m/s 75% 45° -R=163 m- 15° -R=128 m- R=255 m R=255 m "L₂ X
In the standing broad jump, one squats and then pushes off with the legs to see how far one can jump. Suppose the extension of the legs from the crouch position is 0.600 m and the acceleration achieved from this position is 1.25 times the acceleration due to gravity, g. How far can they jump? State
Gun sights are adjusted to aim high to compensate for the effect of gravity, effectively making the gun accurate only for a specific range.(a) If a gun is sighted to hit targets that are at the same height as the gun and 100.0 m away, how low will the bullet hit if aimed directly at a target 150.0
The world long jump record is 8.95 m (Mike Powell, USA, 1991). Treated as a projectile, what is the maximum range obtainable by a person if he has a take-off speed of 9.5 m/s? State your assumptions.
A football quarterback is moving straight backward at a speed of 2.00 m/s when he throws a pass to a player 18.0 m straight downfield.(a) If the ball is thrown at an angle of 25° relative to the ground and is caught at the same height as it is released, what is its initial speed relative to the
Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B , as in
Two campers in a national park hike from their cabin to the same spot on a lake, each taking a different path, as illustrated below. The total distance traveled along Path 1 is 7.5 km, and that along Path 2 is 8.2 km. What is the final displacement of each camper? Path 2 VA 40° X S S= 5.0 km Path
Suppose you first walk 12.0 m in a direction 20° west of north and then 20.0 m in a direction 40.0° south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the
If an airplane pilot is told to fly 123 km in a straight line to get from San Francisco to Sacramento, explain why he could end up anywhere on the circle shown in Figure 3.48. What other information would he need to get to Sacramento? Point Arena W N San Francisco zato S Healdsburg 4 Santa
Refer to Figure 3.43, which shows a boat trying to go straight across the river. Let us calculate the magnitude and direction of the boat's velocity relative to an observer on the shore, vtot. The velocity of the boat, Vboat, is 0.75 m/s in the y-direction relative to the river and the velocity of
Repeat the problem above, but reverse the order of the two legs of the walk; show that you get the same final result. That is, you first walk leg B, which is 20.0 m in a direction exactly 40° south of west, and then leg A, which is 12.0 m in a direction exactly 20° west of north. (This problem
Calculate the wind velocity for the situation shown in Figure 3.44. The plane is known to be moving at 45.0 m/s due north relative to the air mass, while its velocity relative to the ground (its total velocity) is 38.0 m/s in a direction 20.0° west of north.StrategyIn this problem, somewhat
Suppose you take two steps A and B (that is, two nonzero displacements). Under what circumstances can you end up at your starting point? More generally, under what circumstances can two nonzero vectors add to give zero? Is the maximum distance you can end up from the starting point A+B the sum of
(a) Repeat the problem two problems prior, but for the second leg you walk 20.0 m in a direction 40.0°).(b) Repeat the problem two problems prior, but now you first walk 20.0 m in a direction 40.0° east of south (which is equivalent to subtracting A from B-that is, to finding R'' = B - A = -R).
Explain why it is not possible to add a scalar to a vector.
An airline passenger drops a coin while the plane is moving at 260 m/s. What is the velocity of the coin when it strikes the floor 1.50 m below its point of release:(a) Measured relative to the plane? (b) Measured relative to the Earth?StrategyBoth problems can be solved with the techniques for
Show that the order of addition of three vectors does not affect their sum. Show this property by choosing any three vectors A, B, and C, all having different lengths and directions. Find the sum A + B + C then find their sum when added in a different order and show the result is the same. (There
Show that the sum of the vectors discussed in Example 3.2 gives the result shown in Figure 3.23.Data given in Example 3.2A woman sailing a boat at night is following directions to a dock. The instructions read to first sail 27.5 m in a direction 66.0° north of east from her current location, and
If you take two steps of different sizes, can you end up at your starting point? More generally, can two vectors with different magnitudes ever add to zero? Can three or more?
Find the magnitudes of velocities vA and vB in Figure 3.52 y Vtot = 6.72 m/s tot 23.0% 26.5° 22.5° VA Vtot = VA + VB VB X
Suppose you add two vectors and . What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude? What relative direction between them produces the resultant with the smallest magnitude? What is the minimum magnitude?
Find the components of vtot along the x- and y-axes in Figure 3.52. y Vtot V tot 6.72 m/s 23.0% 26.5° 22.5° VA Vtot = VA + VB VB X
Give an example of a nonzero vector that has a component of zero.
Explain why a vector cannot have a component greater than its own magnitude.
Find the components of vtot along a set of perpendicular axes rotated 30° counterclockwise relative to those in Figure 3.52. y Vtot V tot 6.72 m/s 23.0% 26.5° 22.5° VA Vtot = VA + VB VB X
If the vectors A and B are perpendicular, what is the component of A along the direction of B? What is the component of B along the direction of A?
Answer the following questions for projectile motion on level ground assuming negligible air resistance (the initial angle being neither 0 nor 90°):(a) Is the velocity ever zero?(b) When is the velocity a minimum? A maximum?(c) Can the velocity ever be the same as the initial velocity at a time
Answer the following questions for projectile motion on level ground assuming negligible air resistance (the initial angle being neither 0° nor 90°): (a) Is the acceleration ever zero?(b) Is the acceleration ever in the same direction as a component of velocity?(c) Is the acceleration ever
Find the north and east components of the displacement from San Francisco to Sacramento shown in Figure 3.54. Point Arena W N San Francisco zato Healdsburg + S Santa Rosa E Sacramento Vallejo S Sarta Cruz 45⁰ Berkeley Oakland S = 123 km Stockton .....East San
For a fixed initial speed, the range of a projectile is determined by the angle at which it is fired. For all but the maximum, there are two angles that give the same range. Considering factors that might affect the ability of an archer to hit a target, such as wind, explain why the smaller angle
Solve the following problem using analytical techniques: Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs
During a lecture demonstration, a professor places two coins on the edge of a table. She then flicks one of the coins horizontally off the table, simultaneously nudging the other over the edge. Describe the subsequent motion of the two coins, in particular discussing whether they hit the floor at
Repeat Exercise 3.16 using analytical techniques, but reverse the order of the two legs of the walk and show that you get the same final result. (This problem shows that adding them in reverse order gives the same result-that is, B+ A = A + B.) Discuss how taking another path to reach the same
What frame or frames of reference do you instinctively use when driving a car? When flying in a commercial jet airplane?
A basketball player dribbling down the court usually keeps his eyes fixed on the players around him. He is moving fast. Why doesn’t he need to keep his eyes on the ball?
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