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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

A sailboat sails from Marblehead Harbor directly east for 45 nautical miles, then 60°south of east for 20.0 nautical miles, returns to an easterly heading for 30.0 nautical miles, and sails 30°east of north for 10.0 nautical miles, then west for 62 nautical miles. At that time the boat becomes
A vector is20.0 m long and makes an angle of 60.0°counterclockwise from the y -axis (on the side of the − x -axis). What are the x - and y -components of this vector?
Vector A has magnitude 4.0 units; vector B has magnitude 6.0 units. The angle between A and B is 60.0°. What is the magnitude of A + B?
Vector A is directed along the positive y -axis and has magnitude √3.0 units. Vector B is directed along the negative x -axis and has magnitude 1.0 unit. (a) What are the magnitude and direction of A + B? (b) What are the magnitude and direction of A - B? (c) What are the x - and y -components of
Vector a has components ax = − 3.0 m/s2 and ay = + 4.0 m/s2. (a) What is the magnitude of a (b) What is the direction of a? Give an angle with respect to one of the coordinate axes.
In Problem 8, let a = 10° and find the magnitude of vector C using the component method. In problem 8 Two vectors, each of magnitude 4.0 cm, are directed at a small angle a below the horizontal as shown. (The grid is 1 cm on a side.) Let C = A + B. Sketch the direction of C and estimate its
In Problem 8, let a = 10° and find the magnitude of vector D using the component method.
Find the x - and y -components of the four vectors shown in the drawing.
Vector A is directed along the positive x -axis and has magnitude 1.73 units. Vector B is directed along the negative x -axis and has magnitude 1.00 unit. (a) What are the magnitude and direction of A + B? (b) What are the magnitude and direction of A − B? (c) What are the magnitude and
The velocity vector of a sprinting cheetah has x - and y -components vx = + 16.4 m/s and vy = − 26.3 m/s. (a) What is the magnitude of the velocity vector? (b) What angle does the velocity vector make with the + x - and − y -axes?
In each of these, the x - and y -components of a vector are given. Find the magnitude and direction of the vector. (a) Ax = − 5.0 m/s, Ay = + 8.0 m/s. (b) Bx = + 120 m, By = − 60.0 m. (c) Cx = − 13.7 m/s, Cy = − 8.8 m/s. (d) Dx =2.3 m/s2, Dy = 6.5 cm/s2.
A vector A has a magnitude of 22.2 cm and makes an angle of 130.0°with the positive x -axis. What are the x - and y -components of this vector?
Vector B has magnitude 7.1 and direction 14°below the + x -axis. Vector C has x -component C x = − 1.8 and y -component C y = − 6.7. Compute (a) The x - and y- components of B; (b) The magnitude and direction of C; (c) The magnitude and direction of C + B; (d) The magnitude and direction
Margaret walks to the store using the following path: 0.500 miles west, 0.200 miles north 0.300 miles east. What is her total displacement? That is, what is the length and direction of the vector that points from her house directly to the store? Use vector components to find the answer.
Jerry bicycles from his dorm to the local fitness center: 3.00 miles east and 2.00 miles north. Cindy's apartment is located 1.50 miles west of Jerry's dorm. If Cindy is able to meet Jerry at the fitness center by bicycling in a straight line, what is the length and direction she must travel?
Repeat Problem 10 using the component (algebraic) method. In problem 10 A scout troop is practicing its orienteering skills with map and compass. First they walk due east for 1.2 km. Next, they walk 45°west of north for 2.7 km. In what direction must they walk to go directly back to their starting
Use the component method to obtain a more accurate description of the sailboat's location in Problem 12. In problem 12 A sailboat sails from Marblehead Harbor directly east for 45 nautical miles, then 60°south of east for 20.0 nautical miles, returns to an easterly heading for 30.0 nautical miles,
You will be hiking to a lake with some of your friends by following the trails indicated on a map at the trailhead. The map says that you will travel 1.6 mi directly north, then 2.2 mi in a direction 35°east of north, then finally 1.1 mi in a direction 15°north of east. At the end of this hike,
A runner times his speed around a circular track with a circumference of 0.478 mi. At the start he is running toward the east and the track starts bending toward the north. If he goes halfway around, he will be running toward the west. He finds that he has run a distance of 0.750 mi in 4.00 min.
Two vectors have magnitudes 3.0 and 4.0. How are the directions of the two vectors related if? (a) The sum has magnitude 7.0, or (b) If the sum has magnitude 5.0? (c) What relationship between the directions gives the smallest magnitude sum and what is this magnitude?
A runner times his speed around a track with a circumference of 0.50 mi. He finds that he has run a distance of 1.00 mi in 4.0 min. What is his (a) Average speed (b) Average velocity magnitude in m/s?
Peggy drives from Cornwall to Atkins Glen in 45 min. Cornwall is 73.6 km from Illium in a direction 25°west of south. Atkins Glen is 27.2 km from Illium in a direction 15°south of west. Using Illium as your origin, (a) Draw the initial and final position vectors, (b) Find the displacement
To get to a concert in time, a harpsichordist has to drive 122 mi in 2.00 h. (a) If he drove at an average speed of 55.0 mi/h in a due west direction for the first 1.20 h, what must be his average speed if he is heading 30.0° south of west for the remaining 48.0 min? (b) What is his average
A bicycle travels 3.2 km due east in 0.10 h, then 4.8 km at 15.0°east of north in 0.15 h, and finally another 3.2 km due east in 0.10 h to reach its destination. The time lost in turning is negligible. What is the average velocity for the entire trip?
A car travels east at 96 km/h for 1.0 h. It then travels 30.0°east of north at 128 km/h for 1.0 h. (a) What is the average speed for the trip? (b) What is the average velocity for the trip?
A speedboat heads west at 108 km/h for 20.0 min. It then travels at 60.0°south of west at 90.0 km/h for 10.0 min. (a) What is the average speed for the trip? (b) What is the average velocity for the trip?
See Problem 9. During Michaela's travel from Killarney to Cork via Mallow, her actual travel time in the car is 48 min. (a) What is her average speed in m/s? (b) What is the magnitude of her average velocity in m/s?
Geoffrey drives from his home town due east at 90.0 km/h for 80.0 min. After visiting a friend for 15.0 min, he drives in a direction 30.0° south of west at 76.0 km/h for 45.0 min to visit another friend. (a) How far is it to his home from the second town? (b) If it takes him 45.0 min to drive
A hawk is flying north at 2.0 m/s with respect to the ground; 10.0 s later, it is flying south at 5.0 m/s. What is its average acceleration during this time interval?
A skydiver is falling straight down at 55 m/s when he opens his parachute and slows to 8.3 m/s in 3.5 s. What is the average acceleration of the skydiver during those 3.5s?
A runner is practicing on a circular track that is 300 m in circumference. From the point farthest to the west on the track, he starts off running due north and follows the track as it curves around toward the east. (a) If he runs halfway around the track and stops at the farthest eastern point of
A car travels three quarters of the way around a circle of radius20.0 m in a time of 3.0 s at a constant speed. The initial velocity is west and the final velocity is south. (a) Find its average velocity for this trip. (b) What is the car's average acceleration during these 3.0s? (c) Explain how
At t = 0, an automobile traveling north begins to make a turn. It follows one-quarter of the arc of a circle with a radius of 10.0 m until, at t = 1.60 s, it is traveling east. The car does not alter its speed during the turn. Find (a) The car's speed, (b) The change in its velocity during the
At the beginning of a 3.0-h plane trip, you are traveling due north at 192 km/h. At the end, you are traveling 240 km/h in the northwest direction (45°west of north).(a) Draw your initial and final velocity vectors. (b) Find the change in your velocity. (c) What is your average acceleration during
John drives 16 km directly west from Orion to Chester at a speed of 90 km/h, then directly south for 8.0 km to Seiling at a speed of 80 km/h, then finally 34 km southeast to Oakwood at a speed of 100 km/h. Assume he travels at constant velocity during each of the three segments. (a) What was the
A particle's constant acceleration is south at 2.50 m/s2. At t = 0, its velocity is 40.0 m/s east. What is its velocity at t = 8.00 s?
A particle's constant acceleration is north at 100 m/s2. At t = 0, its velocity vector is 60 m/s east. At what time will the magnitude of the velocity be 100 m/s?
A baseball is thrown horizontally from a height of 9.60 m above the ground with a speed of 30.0 m/s. Where is the ball after 1.40 s has elapsed?
A clump of soft clay is thrown horizontally from 8.50 m above the ground with a speed of 20.0 m/s. Where is the clay after 1.50 s? Assume it sticks in place when it hits the ground.
A tennis ball is thrown horizontally from an elevation of 14.0 m above the ground with a speed of 20.0 m/s. (a) Where is the ball after 1.60 s? (b) If the ball is still in the air, how long before it hits the ground and where will it be with respect to the starting point once it lands?
A ball is thrown from a point 1.0 m above the ground. The initial velocity is 19.6 m/s at an angle of 30.0°above the horizontal. (a) Find the maximum height of the ball above the ground. (b) Calculate the speed of the ball at the highest point in the trajectory.
Two displacement vectors each have magnitude 20 km. One is directed 60°above the + x -axis; the other is directed 60°below the + x -axis. What is the vector sum of these two displacements? Use graph paper to find your answer.
An arrow is shot into the air at an angle of 60.0°above the horizontal with a speed of 20.0 m/s. (a) What are the x - and y -components of the velocity of the arrow 3.0 s after it leaves the bowstring? (b) What are the x - and y -components of the displacement of the arrow during the 3.0-s
You are working as a consultant on a video game designing a bomb site for a World War I airplane. In this game, the plane you are flying is traveling horizontally at 40.0 m/s at an altitude of 125 m when it drops a bomb. (a) Determine how far horizontally from the target you should release the
You have been employed by the local circus to plan their human cannonball performance. For this act, a spring-loaded cannon will shoot a human projectile, the Great Flyinski, across the big top to a net below. The net is located 5.0 m lower than the muzzle of the cannon from which the Great
A cannonball is catapulted toward a castle. The cannonball's velocity when it leaves the catapult is 40 m/s at an angle of 37°with respect to the horizontal and the cannonball is 7.0 m above the ground at this time. (a) What is the maximum height above the ground reached by the cannonball? (b)
After being assaulted by flying cannonballs, the knights on the castle walls (12 m above the ground) respond by propelling flaming pitch balls at their assailants. One ball lands on the ground at a distance of 50 m from the castle walls. If it was launched at an angle of 53°above the horizontal,
From the edge of the rooftop of a building, a boy throws a stone at an angle 25.0°above the horizontal. The stone hits the ground 4.20 s later, 105 m away from the base of the building. (Ignore air resistance.) (a) For the stone's path through the air, sketch graphs of x, y, vx, and vy as
Two angles are complementary when their sum is 90.0°.Find the ranges for two projectiles launched with identical initial speeds of 36.2 m/s at angles of elevation above the horizontal that are complementary pairs.(a) For one trial, the angles of elevation are 36.0°and 54.0°. (b) For the second
The range R of a projectile is defined as the magnitude of the horizontal displacement of the projectile when it returns to its original altitude. (In other words, the range is the distance between the launch point and the impact point on flat ground.) A projectile is launched at t = 0 with initial
Use the expression in Problem 57 to find(a) The maximum range of a projectile with launch speed vi and(b) The launch angle q at which the maximum range occurs.In problem 57The range R of a projectile is defined as the magnitude of the horizontal displacement of the projectile when it returns to its
A projectile is launched at t = 0 with initial speed vi at an angle q above the horizontal.(a) What are v x and v y at the projectile's highest point?(b) Find the time t at which the projectile reaches its maximum height.(c) Show that the maximum height H of the projectile is
Orville walks 320 m due east. He then continues walking along a straight line, but in a different direction, and stops200 m northeast of his starting point. How far did he walk during the second portion of the trip and in what direction?
A ballplayer standing at home plate hits a baseball that is caught by another player at the same height above the ground from which it was hit. The ball is hit with an initial velocity of 22.0 m/s at an angle of 60.0° above the horizontal. (a) How high will the ball rise? (b) How much time will
You are planning a stunt to be used in an ice skating show. For this stunt a skater will skate down a frictionless ice ramp that is inclined at an angle of 15.0° above the horizontal. At the bottom of the ramp, there is a short horizontal section that ends in an abrupt drop off. The skater is
A suspension bridge is 60.0 m above the level base of a gorge. A stone is thrown or dropped from the bridge. Ignore air resistance. At the location of the bridge g has been measured to be 9.83 m/s2. (a) If you drop the stone, how long does it take for it to fall to the base of the gorge? (b) If
A circus performer is shot out of a cannon and flies over a net that is placed horizontally 6.0 m from the cannon. When the cannon is aimed at an angle of 40° above the horizontal, the performer is moving in the horizontal direction and just barely clears the net as he passes over it. What is the
Show that for a projectile launched at an angle of 45° the maximum height of the projectile is one quarter of the range (the distance traveled on flat ground).
Two cars are driving toward each other on a straight, flat Kansas road. The Jeep Wrangler is traveling at 82 km/h north and the Ford Taurus is traveling at 48 km/h south, both measured relative to the road. What is the velocity of the Jeep relative to an observer in the Ford?
Two cars are driving toward each other on a straight and level road in Alaska. The BMW is traveling at 100.0 km/h north and the VW is traveling at 42 km/h south, both velocities measured relative to the road. At a certain instant, the distance between the cars is 10.0 km. Approximately how long
A car is driving directly north on the freeway at a speed of 110 km/h and a truck is leaving the freeway driving 85 km/h in a direction that is 35° west of north. What is the velocity of the truck relative to the car?
A Nile cruise ship takes 20.8 h to go upstream from Luxor to Aswan, a distance of 208 km, and 19.2 h to make the return trip downstream. Assuming the ship's speed relative to the water is the same in both cases, calculate the speed of the current in the Nile.
Vectors A, B, and C are shown in the figure.(a) Draw vectors D and E, where D = A + B and E = A + C.(b) Show that A + B = B + A by graphical means.
A small plane is flying directly west with an airspeed of 30.0 m/s. The plane flies into a region where the wind is blowing at 10.0 m/s at an angle of 30° to the south of west. (a) If the pilot does not change the heading of the plane, what will be the ground speed of the airplane? (b) What will
A small plane is flying directly west with an airspeed of 30.0 m/s. The plane flies into a region where the wind is blowing at 10.0 m/s at an angle of 30° to the south of west. In that region, the pilot changes the directional heading to maintain her due west heading. (a) What is the change she
A boat that can travel at 4.0 km/h in still water crosses a river with a current of 1.8 km/h. At what angle must the boat be pointed upstream to travel straight across the river? In other words, in what direction is the velocity of the boat relative to the water?
At an antique car rally, a Stanley Steamer automobile travels north at 40 km/h and a Pierce Arrow automobile travels east at 50 km/h. Relative to an observer riding in the Stanley Steamer, what are the x - and y -components of the velocity of the Pierce Arrow car? The x -axis is to the east and the
Sheena can row a boat at 3.00 mi/h in still water. She needs to cross a river that is 1.20 mi wide with a current flowing at 1.60 mi/h. Not having her calculator ready, she guesses that to go straight across, she should head 60.0° upstream. (a) What is her speed with respect to the starting point
A dolphin wants to swim directly back to its home bay, which is 0.80 km due west. It can swim at a speed of 4.00 m/s relative to the water, but a uniform water current flows with speed 2.83 m/s in the southeast direction. (a) What direction should the dolphin head? (b) How long does it take the
Demonstrate with a vector diagram that a displacement is the same when measured in two different reference frames that are at rest with respect to each other.
A boy is attempting to swim directly across a river; he is able to swim at a speed of 0.500 m/s relative to the water. The river is 25.0 m wide and the boy ends up at 50.0 m downstream from his starting point. (a) How fast is the current flowing in the river? (b) What is the speed of the boy
An aircraft has to fly between two cities, one of which is 600.0 km north of the other. The pilot starts from the southern city and encounters a steady 100.0 km/h wind that blows from the northeast. The plane has a cruising speed of 300.0 km/h in still air. (a) In what direction (relative to east)
Jason is practicing his tennis stroke by hitting balls against a wall. The ball leaves his racquet at a height of 60 cm above the ground at an angle of 80° with respect to the vertical. (a) The speed of the ball as it leaves the racquet is 20 m/s and it must travel a distance of 10 m before it
Two vectors, each of magnitude 4.0 cm, are directed at a small angle a below the horizontal as shown. (The grid is 1 cm on a side.)(a) Let C = A + B. Sketch the direction of C and estimate its magnitude.(b) Let D = A - B. Sketch the direction of D and estimate its magnitude.
Imagine a trip where you drive along an east-west highway at 80.0 km/h for 45.0 min and then you turn onto a highway that runs 38.0° north of east and travel at 60.0 km/h for 30.0 min. (a) What is your average velocity for the trip? (b) What is your average velocity on the return trip when you
A jetliner flies east for 600.0 km, then turns 30.0° toward the south and flies another 300.0 km. (a) How far is the plane from its starting point? (b) In what direction could the jetliner have flown directly to the same destination (in a straight-line path)? (c) If the jetliner flew at a
An African swallow carrying a very small coconut is flying horizontally with a speed of 18 m/s. (a) If it drops the coconut from a height of 100 m above the Earth, how long will it take before the coconut strikes the ground? (b) At what horizontal distance from the release point will the coconut
A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 320 km from Athens in the direction 20.0° N of E. The pilot heads directly for Sparta and flies at an airspeed of 160 km/h. After flying for 2.0 h, the pilot expects to be at Sparta, but instead he finds himself 20
The citizens of Paris were terrified during World War I when they were suddenly bombarded with shells fired from a long-range gun known as Big Bertha. The barrel of the gun was 36.6 m long and it had a muzzle speed of 1.46 km/s. When the gun's angle of elevation was set to 55°, what would be the
You are serving as a consultant for the newest James Bond film. In one scene, Bond must fire a projectile from a cannon and hit the enemy headquarters located on the top of a cliff 75.0 m above and 350 m from the cannon. The cannon will shoot the projectile at an angle of 40.0° above the
The pilot of a small plane finds that the airport where he intended to land is fogged in. He flies 55 mi west to another airport to find that conditions there are too icy for him to land. He flies 25 mi at 15° east of south and is finally able to land at the third airport. (a) How far and in what
A particle has a constant acceleration of 5.0 m/s2 to the east. At time t = 0, it is 2.0 m east of the origin and its velocity is 20 m/s north. What are the components of its position vector at t = 2.0 s?
A baseball batter hits a long fly ball that rises to a height of 44 m. An outfielder on the opposing team can run at 7.6 m/s. What is the farthest the fielder can be from where the ball will land so that it is possible for him to catch the ball?
A locust jumps at an angle of 55.0° and lands 0.800 m from where it jumped. (a) What is the maximum height of the locust during its jump? Ignore air resistance. (b) If it jumps with the same initial speed at an angle of 45.0°, would the maximum height be larger or smaller? (c) What about the
Michaela is planning a trip in Ireland from Killarney to Cork to visit Blarney Castle. She also wants to visit Mallow, which is located 39 km due east of Killarney and 22 km due north of Cork. Draw the displacement vectors for the trip when she travels from Killarney to Mallow to Cork. (a) What
A helicopter is flying horizontally at 8.0 m/s and an altitude of 18 m when a package of emergency medical supplies is ejected horizontally backward with a speed of 12 m/s relative to the helicopter. Ignoring air resistance, what is the horizontal distance between the package and the helicopter
An airplane is traveling from New York to Paris, a distance of 5.80 × 103 km. Ignore the curvature of the Earth. (a) If the cruising speed of the airplane is 350.0 km/h, how much time will it take for the airplane to make the round-trip on a calm day? (b) If a steady wind blows from New York to
A gull is flying horizontally 8.00 m above the ground at 6.00 m/s. The bird is carrying a clam in its beak and plans to crack the clamshell by dropping it on some rocks below. Ignoring air resistance, (a) What is the horizontal distance to the rocks at the moment that the gull should let go of the
A beanbag is thrown horizontally from a dorm room window a height h above the ground. It hits the ground a horizontal distance h (the same distance h) from the dorm directly below the window from which it was thrown. Ignoring air resistance, find the direction of the beanbag's velocity just before
In a plate glass factory, sheets of glass move along a conveyor belt at a speed of 15.0 cm/s. An automatic cutting tool descends at preset intervals to cut the glass to size. Since the assembly belt must keep moving at constant speed, the cutter is set to cut at an angle to compensate for the
A pilot wants to fly from Dallas to Oklahoma City, a distance of 330 km at an angle of 10.0° west of north. The pilot heads directly toward Oklahoma City with an air speed of 200 km/h. After flying for 1.0 h, the pilot finds that he is 15 km off course to the west of where he expected to be after
A ball is thrown horizontally off the edge of a cliff with an initial speed of 20.0 m/s. (a) How long does it take for the ball to fall to the ground 20.0 m below? (b) How long would it take for the ball to reach the ground if it were dropped from rest off the cliff edge? (c) How long would it take
A marble is rolled so that it is projected horizontally off the top landing of a staircase. The initial speed of the marble is 3.0 m/s. Each step is 0.18 m high and 0.30 m wide. Which step does the marble strike first?
A motor scooter rounds a curve on the highway at a constant speed of 20.0 m/s. The original direction of the scooter was due east; after rounding the curve the scooter is heading 36° north of east. The radius of curvature of the road at the location of the curve is 150 m. What is the average
You want to make a plot of the trajectory of a projectile.That is, you want to make a plot of the height y of the projectile as a function of horizontal distance x. The projectile is launched from the origin with an initial speed vi at an angle q above the horizontal. Show that the equation of the
Explain the need for automobile seat belts in terms of Newton's first law.
A freight train consists of an engine and several identical cars on level ground. Determine whether each of these statements is correct or incorrect and explain why. (a) If the train is moving at constant speed, the engine must be pulling with a force greater than the train's weight. (b) If the
(a) Does a man weigh more at the North Pole or at the equator? (b) Does he weigh more at the top of Mt. Everest or at the base of the mountain?
What is the acceleration of an object thrown straight up into the air at the highest point of its motion? Does the answer depend on whether air resistance is negligible or not? Explain.
If a wagon starts at rest and pulls back on you with a force equal to the force you pull on it, as required by Newton's third law, how is it possible for you to make the wagon start to move? Explain.

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