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physics
mechanics

Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions

A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level ground: d1 for 0.40 m southwest (that is, at 45o from directly south and from directly west), d2 for 0.50 m due east, d3 for 0.60 m at 60o north of east. Let the positive x direction be east and the
In Fig. 3-32, a cube of edge length a sirs with one corner at the origin of an xyz coordinate system. A body diagonal is a line that extends from one corner to another through the center. In unit-vector notation, what is the body diagonal that extends from the cornet at? (a) Coordinates (0, 0,
In Fig. 3-33, a vector a with a magnitude of 17.0m is directed at angle θ = 56.0o counter clock-wise from the + x axis. What are the components? (a) ax and (b) ay of the vector? A second co-ordinate system is inclined by angle θ = 18.0o with respect to the first. What are the components? (c) ax'
Two vectors, r and s, lie in the xy plane. Their magnitudes are 4.50 and 7 .30 units, respectively, and their directions are 320o and 85.0o, respectively, as measured counterclockwise from the positive x axis. What are the values of?(a) r ∙ s and(b) r x s?
Two vectors are given by a = 3.0i + 5.0j and b = 2.0i + 4.0i. Find(a) a x b,(b) a ∙ b,(c) (a + b) ∙ b, and(d) The component of a along the direction of 6.
Displacement d1 is in the yz plane 63.0o from the positive direction of the y axis, has a positive z component, and has a magnitude of 4.50 m. Displacement d2 is in the xz plane 30.0o from the positive direction of the x axis, has a positive z component, and has magnitude I.40 m. What are(a) d1 and
Use the definition of scalar product, a ∙ b = ab cos θ, and the fact that a ∙ b = axbx + ayby + azbz to calculate the angle between the two vectors given by a = 3.0i + 3.0j + 3.0k and b = 2.0i + 1.0j + 3.0k.
For the following three vectors, what is 3C ∙ (2A x B)? A = 2.00i + 3.00j – 4.00k B = –3.00i + 4.00j + 2.00k C= 7.00i – 8.00j.
Vector A has a magnitude of 6.00 units, vector B has a magnitude of 7.00 units, and A ∙ B has a value of 14.0. What is the angle between the directions A and B?
In the product F = qv x B, take q = 2, v = 2.0i + 4.0j + 6.0k and F = 4.0i = 20j + 12k. What then is B in unit-vector notation if Bx = By?
The three vectors in Fig. 3-35 have magnitudes a = 10.0m and angle θ = 30.0o. What are? (a) The x component and (b) The y component of a; (c) The x component and (d) The y component of b; and (e) The x componenet and (f) The y compoenent of c? If c = pa + qb, what are the values of (g) p and (h) q?
In a meeting of mimes, mime 1 goes through a displacement d1 = (4.0 m)i + (5.0 m)j and mime 2 goes through a displacement d2 = (– 3.0 m)i + (4.0 m)i. What are?(a) d1 x d2(b) d1 ∙ d2(c) (d1 + d2) and(d) The component of d1 along the direction of d2?
Rock faults are ruptures along which opposite faces of have slid past each other. In Fig. 3-36, points .4 and B coincided before the rock in the foreground slid down to the right. The net displacement B is along the plane of the fault. The horizontal component of B is the strike-slip AC. The
Two vectors a and b have the components, in meters, ax = 3.2, ay = 1.6, bx = 0.50, by = 4.5.(a) Find the angle between the directions of a and b. There are two vectors in the xy plane that are perpendicular to a and have a magnitude of 5.0m. One, vector Z, has a positive x component and the other,
A vector d of magnitude 10 units and another vector b of magnitude 6.0 units differ in directions by 60o. Find(a) The scalar product of the two vectors and(b) The magnitude of the vector product a x b.
Vector a has a magnitude of 5.0m and is directed east. Vector b has a magnitude of 4.0m and is directed 35o west of due north, what are?(a) The magnitude and(b) The direction of a + b, what are?(c) The magnitude and(d) The direction of b – a?(e) Draw a vector diagram for each combination.
A particle undergoes three successive displacements in a plane, as follows: d1, 4.00m southwest; then d2, 5.00m east; and finally d3, 6.00m in a direction 60.0o north of east. Choose a coordinate system with the y axis pointing north and the x axis pointing east. What are?(a) The x component and(b)
A sailboat sets out from the U.S side of Lake Erie for a point on the Canadian side, 90.0km due north. The sailor, however, ends up 50.0km due east of the starting point.(a) How far and(b) In what direction must the sailor now sail to reach the original destination?
Find the sum of the following, four vectors in (a) Unit-vector notation and as (b) A magnitude and (c) An angle relative to + x.
Vectors A and B lie in an xy plane. A has magnitude 8.00 and angle 130o; B has components Bx = – 7.72 and By =– 9.20. What are the angles between the negative direction of the y axis and(a) The direction of A,(b) The direction of the product A x B, and(c) The direction of A x (B + 3.00k)
Vectors A and B lie in an xy plane. A has magnitude 8.00 and angle 130o; B has components Bx = ?? 7.72 and By = ?? 9.20. (a) What is 5A ?? B? What is 4A x 3B in? (b) Unit-vector notation and (c) Magnitude-angle notation with spherical coordinates (See Fig. 3-37)? (d) What is the angle between the
Vectors d1 is in the negative direction of a y axis, and vector d2 is in the positive direction of an x axis. What is the direction of?(a) d2/4 and(b) d1/(– 4)? What are the magnitudes of products?(c) d1 ∙ d2 and(d) d1 ∙ (d2/4? What is the direction of the vector resulting from?(e) d1 x d2
Here are three vectors in meters; what results from (a) d1 ??(d2+ d3), (b) d1 ?? (d2 x d3) and (c) d1 x (d2 + d3)?
A golfer takes three putts to get the ball into the hole. The first putt displaces the ball 3.66 m north, the second 1.83 m southeast, and the third 0.91 m southwest. What are?(a) The magnitude and(b) The direction of the displacement needed to get the ball into the hole on the first putt?
Consider a in the positive direction of x, b in the positive direction of y, and a scalar d. What is the direction of b/d if d and(a) Positive and(b) Negative? What is the magnitude of?(c) a ∙ b and(d) a ∙ b/d? What is the direction of the vector resulting from?(e) a x b and(f) b x a?(g) What
A vector d has a magnitude of 2.5 m and points north. What are?(a) Magnitude and(b) The direction of 4.0d? What are?(c) The magnitude and(d) The direction of – 3.0d?
Let i be directed to the east, j be directed to the north, and k be directed upward. What are the values of products?(a) i ∙ k(b) (– k) ∙ (– j), and(c) j ∙ (– j)? What are the directions (such as east or down) of products?(d) k x j,(e) (–i) x (– j), and(f) (– k) x (–j)?
Consider two displacements, one of magnitude 3m and another of magnitude 4 m. Show how the displacement vectors may be combined to get a resultant displacement of magnitude(a) 7 m,(b) 1 m, and(c) 5 m.
A bank in downtown Boston is robbed (see the map in Fig. 3-38). To elude police, the robbers escape by helicopter, making three successive flights described by the following displacements: 32km, 45o south of east; 53 km, 26o north of west; 26 km, l-8o east of south. At the end of the third flight
If B is added to A, the result is 6.0i + 1.0i. If B is subtracted from A the result is – 4.0i + 7.0j.What is the magnitude of A?
A has the magnitude 12.0m and is angled 60.0o counterclockwise from the positive direction of the x axis of arl xy coordinate system. Also, B = (12.0 m)i + (8.00 -)j on that same coordinate system. We now rotate the system counterclockwise about the origitly 20.0o to form an x'y' system. On this
A woman walks 250 m in the direction 30o east of north, then 175 m directly east. Find(a) The magnitude and(b) The angle of her final displacement from the starting point.(c) Find the distance she walks.(d) Which is greater, that distance or the magnitude of her displacement?
A vector d has a magnitude 3.0 m and is directed south. What are?(a) The magnitude and(b) The direction of the vector 5.0d? What are?(c) The magnitude and(d) The direction of the vector – 2.0d?
A positron undergoes a displacement ∆r = 2.0i – 3.0j + 6.0k, ending with the position vector r = 3.0j - 4.0k, in meters. What was the positron's initial position vector?
A watermelon seed has the following coordinates: x = – 5.0m, y = 8.0m, and z – 0 m. Find its position vector(a) In unit-vector notation and as(b) A magnitude and(c) An angle relative to the positive direction of the x axis.(d) Sketch the vector on a right-handed coordinate system. If the seed
The position vector for an electron is R = (5.0 m)i – (3.0 m)j + (2.0 m)k.(a) Find the magnitude of 7.(b) Sketch the vector on a right-handed coordinate system.
The minute hand of a wall clock measures 10 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the(a) Magnitude and(b) Angle from a quarter after the hour to half past, the(c)
An ion's position vector is initially r = 5.0i – 6.0j + 2.0k, and 10 s later it is r = –2.0i + 8.0j – 2.0k, all in meters. In unit-vector notation, what is its vavg during the 10s?
An electron's position is given by r = 3.00ti – 4.00t2j + 2.00k, with t in seconds and r in meters. (a) In unit vector notation, what is the electron's velocity v (t)? At t = 2.00 s, what is v (b) In unit-vector notation and as (c) A magnitude and (d) An angle relative to the
A train at a constant 60.0 km/h moves east for 40.0 min, then in a direction 50.0o east of due north for 20.0 min, and then west for 50.0 min. What are the (a) Magnitude and(b) Angle of its average velocity during this trip?
A plane flies 483 km east from city A to city B in 45.0 min and then 966 km south from city B to city C in 1.50 h. For the total trip, what are the(a) Magnitude and(b) Direction of the plane's displacement, the(c) Magnitude and(d) Direction of its average velocity, and(e) Its average speed?
A particle moves so that its position (in meters) as a function of time (in seconds) is r = i + 4t2j + tk. Write expressions for (a) Its velocity and(b) Its acceleration as functions of time.
The position r of a particle moving in an xy plane is given by r = (2.00t3 – 5.00r)i + (6.00 – 7.00t4)j, with r in meters and t in seconds. In unit-vector notation, calculate (a) r, (b) v, and (c) a for t = 2.00s. (d) What is the angle between the positive direction of the x
At one instant a bicyclist is 40.0 m due east of a park's flagpole, going due south with a speed of 10.0 m/s. Then 30.0s later, the cyclist is 40.0 m due north of the flagpole, going due east with a speed of 10.0 m/s. For the cyclist in this 30.0s interval, what are the(a) Magnitude and(b)
A cart is propelled over an xy plane with acceleration components ax = 4.0m/2 and ay = –2.0m/s2. Its initial velocity has components v0x = 8.0 m/s and v0y = 12m/s. In unit-vector notation, what is the velocity of the cart when it reaches its greatest y coordinate?
A moderate wind accelerates a pebble over a horizontal xy plane with a constant acceleration a = (5.00 m/s2)i + (7.00m/s2)j. At time t = 0, the velocity is (4.00m/s)i. What are the (a) Magnitude and(b) Angle of its velocity when it has been displaced by 12.0 m parallel to the x axis?
A particle leaves the origin with an initial velocity v = (3.00i) m/s and a constant a = (– 1.00i – 0.500j) m/s2. When it reaches its coordinate, what are its (a) Velocity and(b) Position vector?
The velocity v of a particle moving in the xy plane is given by v = (6.0t – 4.02)i + 8.0j , with v in meters per second and t (> 0) in seconds.(a) What is the acceleration when t = 3.0 s?(b) When (if ever) is the acceleration zero?(c) When (if ever) is the velocity zero?(d) When (if ever) does
The acceleration of a particle moving only on a horizontal xy plane is given by a = 3ti + 4tj, where a is in meters per second-squared and t is in seconds. At t = 0, the position vector r = (20.0m)i + (40.0m)j locates the particle, which then has the velocity vector v = (5.00m/s)i + (2.00m/s)j. At
In Fig. 4-35, particle A moves along the line y = 30 m with a constant velocity v of magnitude 3.0 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration d of magnitude 0.40m/s2. What angle g
A projectile is fired horizontally from a gun that is 45.0 m above flat ground, emerging from the gun with a speed of 250 m/s.(a) How long does the projectile remain in the air?(b) At what horizontal distance from the firing point does it strike the ground?(c) What is the magnitude of the vertical
In the 1991 World Track and Field Championships in Tokyo, Mike Powell jumped 8.95 m, breaking by a full 5 cm the 23-year long-jump record set by Bob Beamon. Assume that Powell's speed on takeoff was 9.5m/s (about equal to that of a sprinter) and that g - 9.80m/s2 in Tokyo. How much less was
A small ball rolls horizontally off the edge of a tabletop that is 1.20 m high. It strikes the floor at a point 1.52 m horizontally from the table edge. (a) How long is the ball in the in air? (b) What is its speed at the instant it leaves the table?
A dart is thrown horizontally with an initial speed of 10m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below P, 0.19 s later.(a) What is the distance PQ?(b) How far away from the dart board is the dart released?
In Fig. 4-36, a stone is projected at a cliff of height h with an initial speed of 42.0 m/s directed at angle θ? = 60.0??above the horizontal. The stone strikes at A 5.50s after launching. Find? (a) The height h of the cliff, (b) The speed of the stone just before impact at A, and (c) The maximum
A certain airplane has a speed of 290.0 km/h and is diving at an angle of θ = 30.0??below the horizontal when the pilot releases a radar decoy (Fig. 4-37). The horizontal distance between the release point and the point where the decoy strikes the ground is d = 700 m.? (a) How long is the decoy in
A stone is catapulted at time t = 0, with an initial velocity of magnitude 20.0 m/s and at an angle of 40.0° above the horizontal. What are the magnitudes of the(a) Horizontal and(b) Vertical components of its displacement from the catapult site at t = 1.10 s? Repeat for the(c) Horizontal and(d)
A lowly high diver pushes off horizontally with a speed of 2.00m/s from the platform edge 10.0m above the surface of the water.(a) At what horizontal distance from the edge is the diver 0.800 s after pushing off?(b) At what vertical distance above the surface of the water is the diver just then?(c)
A plane, diving with constant speed at an angle of 53.0° with the vertical, releases a projectile at an altitude of 730 m. The projectile hits the ground 5.00s after release.(a) What is the speed of the plane?(b) How far does the projectile travel horizontally during its flight? What are the(c)
A soccer ball is kicked from the ground with an initial speed of 19.5 m/s at an upward angle of 45°. A player 55 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground?
A projectile's launch speed is five times its speed at maximum height. Find launch angle θ0.
A ball is shot from the ground into the air. At u height of 9.1m, its velocity is v = (7.6i + 6.1j)m/s, with i horizontal and j upward.(a) To what maximum height does the ball rise?(b) What total horizontal distance does the ball travel? What are the(c) Magnitude and(d) Angle (below the horizontal)
You throw a ball toward a wall at speed 25.0 m/s and at angle θ0 = 40.0o above the horizontal (Fig. 4-38). The wall is distance d = 22.0m from the release point of the ball. (a) How far above the release point does the ball hit the wall? What are the (b) Horizontal and (c) Vertical components of
A rifle that shoots bullets at 460 m/s is to be aimed at a target 45.7 m away. If the center of the target is level with the rifle, how high above the target must the rifle barrel be pointed so that the bullet hits dead center?
A baseball leaves a pitcher's hand horizontally at a speed of 161 km/h. The distance to the batter is 18.3 m.(a) How long does the ball take to travel the first half of that distance?(b) The second half?(c) How far does the ball fall freely during the first half?(d) During the second half?(e) Why
In Fig. 4-39, a ball is thrown leftward from the left edge of the roof, at height h above the ground. The ball hits the ground 1.50 s later, at distance d = 25.0m from the building and at angle θ = 60.0? with the horizontal (a) Find h. What are the (b) Magnitude and (c) Angle relative to the
A golf ball is struck at ground level. The speed of the golf ball as a function of the time is shown in Fig. 4-40, where t = 0 at the instant the ball is struck.(a) How far does the golf ball travel horizontally before returning to ground level?(b) What is the maximum height above ground level
In Fig. 4-41, a ball is launched with a velocity of magnitude 10.0m/s, at an angle of 50.0oto the horizontal. The launch point is at the base of a ramp of horizontal length d1= 6.00 m and height d2= 3.60m. A plateau is located at the top of the ramp.? (a) Does the ball land on the ramp or the
In Fig. 4-44, a ball is thrown up onto a roof, landing 4.00 s later at height h = 20.0 m above the release level. The ball's path just before landing is angled at θ = 60.0? with the roof. (a) Find the horizontal distance d it travels. (See the hint to Problem 41) What are the (b) Magnitude and (c)
A batter hits a pitched ball when the center of the ball is 1.22 m above the ground. The ball leaves the bat at an angle of 45o with the ground. With that launch, the ball should have a horizontal range (returning to the launch level) of 107 m. (a) Does the ball clear a7.32-m-high fence that is
A ball is to be shot from level ground toward a wall at distance x (Fig.4-46a). Figure 4-46b shows the y component v, of the ball's velocity just as it would reach the wall, as a function of that distance x. What is the launchangle?
A football kicker can give the ball an initial speed of 25m/s. What are the (a) Least and (b) Greatest elevation angles at which he can kick the ball to score a field goal from a point 50 m in front of goalposts whose horizontal bar is 3.44 m above the ground?
If the 1 kg standard body has an acceleration of 2.00 m/s2 at20.0o to the positive direction of an x axis, what are?(a) The x component and(b) The y component of the net force acting on the body, and(c) What is the net force in unit-vector notation?
Two horizontal forces act on a 2.0 kg chopping block that can slide over a frictionless kitchen counter, which lies in an xy plane. One force is F1 = (3.0N)i + (4.0N)i. Find the acceleration of the chopping block in unit-vector notation when the other force is(a) F2 = (– 3.0 N)i + (– 4.0
Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 9.0 N acting due east, and the other is 8.0 N acting 62o north of west. What is the magnitude of the body's acceleration?
A 2.00 kg object is subjected to three forces that give acceleration a = – (8.00 m/s2)i + (6.00 m/s2)i. If two of the three forces are F1 = (30.0 N)i + (16.0 N)j and F2 = (12.0N)i + (8.00 N)j find the third force.
There are two forces on the 2.00 kg box in the overhead view of Figure, but only one is shown. For F1 = 20.0 N, a = 12.0 m/s2, and θ = 30.0o, find the second force (a) In unit-vector notation and as (b) A magnitude and (c) An angle relative to the positive direction of the x axis.
While two forces act on it, a particle is to move at the constant velocity v = (3 m/s)i – (4 m/s)j. One of the forces is F1 = (2 N)i + (– 6 N)j. What is the other force?
Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces shown in Figure, with F1 = 32N, F2 = 55N, F3 = 41N, θ1 = 30o, and θ3 = 60o. What is the asteroid's acceleration? (a) In unit-vector notation and as (b) A magnitude and (c)
In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of Figure. The tire remains stationary in spite of the three pulls. Alex pulls with force FA of magnitude 220 N and Charles pulls with force F, of magnitude 170
A 2.0 kg particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by x = 3.0m + (4.0 m/s)t + ct2 – (2.0 m/s3)t3, with x in meters and t in seconds. The factor c is a constant. At t = 3.0 s, the force on the particle has a magnitude of 36N
A 0.150 kg particle moves along an x axis according to x(t) = – 13.00 + 2.00t + 4.00t2 – 3.00t3, with x in meters and t in seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.40 s?
A 0.340 kg particle moves in an xy plane according to x(t) = – 15.00 + 2.00t – 4.00t3 and y(t) = 25.00 + 7.00t – 9.00t2 ,with x and y in meters and / in seconds. At t = 0.700s, what are(a) The magnitude and(b) The angle (relative to the positive direction of the x axis) of the net force on
Two horizontal forces F1 and F2 act on a 4.0 kg disk that slides over frictionless ice, on which an xy coordinate system is laid out. Force F1 is in the positive direction of the x axis and has a magnitude of 7.0 N. Force F2 has a magnitude of 9.0N. Figure gives the x component vx of the velocity
(a) An 11.0kg salami is supported by a cord that runs to a spring scale, which is supported by a cord hung from the ceiling (Figure a). What is the reading on the scale, which is marked in weight units? (b) In Figure b the salami is supported by a cord that runs around a pulley and to a scale. The
A block with a weight of 3.0 N is at rest on a horizontal surface. A 1.0 N upward force is applied to the block by means of an attached vertical string. What are the(a) Magnitude and(b) Direction of the force of the block on the horizontal surface?
Figure shows an arrangement in which four disks are suspended by cords. The longer, top cord loops over a frictionless pulley and pulls with a force of magnitude 98 N on the wall to which it is attached. The tensions in the shorter cords are T1 = 58.8 N T2 = 49.0 N, and T3 = 9.8 N. What are the
(a) What is the ratio of the tension in each tibia (forepart of a leg) to the insect's weight? (b) If the insect straightens out its legs somewhat, does the tension in each tibia increase, decrease, or stay the same?
A customer sits in an amusement park ride in which the compartment is to be pulled downward in the negative direction of a y axis with an acceleration magnitude of 1 .24g, with g = 9.80 m/s2. A 0.567g coin rests on the customer's knee. Once the motion begins and in unit-vector notation, what is the
Tarzan, who weighs 820 N, swings from a cliff at the end of a 20.0 m vine that hangs from a high tree limb and initially makes an angle of 22.0o with the vertical assume that an x axis extends horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the
In Figure, let the mass of the block be 8.5 kg and the angle θ be 30o. Find (a) The tension in the cord and (b) The normal force acting on the block. (c) If the cord is cut, find the magnitude of the resulting acceleration of the block.
There are two horizontal forces on the 2.0 kg box in the overhead view of Figure but only one (of magnitude F1 = 20 N) is shown. The box moves along the x axis. For each of the following values for the acceleration ax of the box, find the second force in unit-vector notation: (a) 10 m/s2, (b) 20
A constant horizontal force Fa pushes a2.00 kg FedEx package across a frictionless floor on which an xy coordinate system has been drawn. Figure gives the package's x and y velocity components versus time t. What are the (a) Magnitude and (b) Direction of Fa?
In April 1974, John Massis of Belgium managed to move two passenger railroad cars. He did so by clamping his teeth down on a bit that was attached to the cars with a rope and then leaning backward while pressing his feet against the railway ties. The cars together weighed 700kN (about 80 tons).
Sun jamming a "sun yacht" is a spacecraft with a large sail that is pushed by sunlight. Although such a push is tiny in everyday circumstances, it can be large enough to send the spacecraft outward from the Sun on a cost-free but slow trip. Suppose that the spacecraft has a mass of 900 kg and
The tension at which a fishing line snaps is commonly called the line's "strength."What minimum strength is needed for a line that is to stop a salmon of weight 85 N in 11 cm if the fish is initially drifting at2.8 m/s? Assume a constant deceleration.
A 500 kg rocket sled can be accelerated at a constant rate from rest to 1600 km/h in 1.8 s. What is the magnitude of the required net force?
A car traveling at 53 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 65 cm (with respect to the road) while being brought to rest by an inflated air bag. What magnitude of force (assumed constant) acts on the passenger's upper torso, which has a mass of 4I kg?
A firefighter who weighs 712 N slides down a vertical pole with an acceleration of 3.00 m/s2, directed downward. What are the(a) Magnitude and(b) Direction (up or down) of the vertical force on the firefighter from the pole and the(c) Magnitude and(d) Direction of the vertical force of the pole on
The high-speed winds around a tornado can drive projectiles into trees, building walls, and even metal traffic signs. In a laboratory simulation, a standard wood toothpick was shot by pneumatic gun into an oak branch. The toothpick's mass was 0.1-3 g, its speed before entering the branch was 220

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