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mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
Solve the triangles with the given parts.a = 0.530, b = 0.875, c = 1.25
Find the indicated vector sums and differences with the given vectors by means of diagrams.A + 2D − 3B A B C D E
A laser on a self-driving car stopped at a traffic signal detects a pedestrian a distance of 15.8 m away. A split second later, the laser rotates by 56.3° and detects a street light pole 12.1 m away. How far is the pedestrian from the street light pole?
Point P on the mechanism shown in Fig. 9.67 is driven back and forth horizontally. If the minimum value of angle θ is 32.0°, what is the distance between extreme positions of P? What is the maximum possible value of angle θ? 36.0 cm 0 Fig. 9.67 24.5 cm P
Assuming the vectors in Fig. 9.49 are in equilibrium, find T1 and T2. See Example 6.Data from Example 6An 865-lb crate of building supplies is hanging from two cables as shown in Fig. 9.38. Find the tensions T1 and T2 assuming that the forces are in equilibrium.The table below shows the x- and
Solve the triangles with the given parts.a = 4114, b = 9110, c = 5016
A ship’s captain notes that a second ship is 14.5 km away at a bearing measured clockwise from true north of 46.3°, and that a third ship was at a distance of 21.7 km at a bearing of 201.0°. How far apart are the second and third ships?
Find the indicated vector sums and differences with the given vectors by means of diagrams.B + 2C − E A B C D E
Two persons are talking to each other on cell phones. The angle between their signals at the tower is 132°, as shown in Fig. 9.79. How far apart are they? Fig. 9.79 2.4 mi www. PATA 132* 3.7 mi
Solve the triangles with the given parts.a = 17, b = 12, c = 25
An air traffic controller sights two planes that are due east from the control tower and headed toward each other. One is 15.8 mi from the tower at an angle of elevation of 26.4°, and the other is 32.7 mi from the tower at an angle of elevation of 12.4°. How far apart are the planes?
Find the indicated vector sums and differences with the given vectors by means of diagrams.2B − 3/2E A B C D E
A person standing on level ground from the base of the Skylon Tower in Niagara Falls observes an elevator going up the side of the tower. At one instant, the angle of elevation to the elevator is 42.5° and then 15.0 s later, the angle of elevation is 60.7°. If the elevator travels at a rate of
Solve the triangles with the given parts.A = 43.12°, a = 7.893, b = 4.113
Find the indicated vector sums and differences with the given vectors by means of diagrams.3B + 1/2A A B C D E
A flat rectangular barge, 48.0 m long and 20.0 m wide, is headed directly across a stream at 4.5 km/h. The stream flows at 3.8 km/h. What is the velocity, relative to the riverbed, of a person walking diagonally across the barge at 5.0 km/h while facing the opposite upstream bank?
The resultant R of displacements A and B is perpendicular to A. If A = 25 m and R = 25 m, find the angle between A and B.
A motorist traveling along a level highway at 75 km/h directly toward a mountain notes that the angle of elevation of the mountain top changes from about 20° to about 30° in a 20-min period. How much closer on a direct line did the mountain top become?
Solve the triangles with the given parts.A = 67.16°, B = 96.84°, c = 532.9
A car is held stationary on a ramp by two forces. One is the force of 480 lb by the brakes, which hold it from rolling down the ramp. The other is a reaction force by the ramp of 2250 lb, perpendicular to the ramp. This force keeps the car from going through the ramp. See Fig. 9.48. What is the
A plane is moving at 75.0 m/s, and a package with weather instruments is ejected horizontally from the plane at 15.0 m/s, perpendicular to the direction of the plane. If the vertical velocity vv (in m/s), as a function of time t (in s) of fall, is given by vv = 9.80t, what is the velocity of the
Find the indicated vector sums and differences with the given vectors by means of diagrams.C − 2A A B C D E
A ferryboat travels at 11.5 km/h with respect to the water. Because of the river current, it is traveling at 12.7 km/h with respect to the land in the direction of its destination. If the ferryboat’s heading is 23.6° from the direction of its destination, what is the velocity of the current?
The angle between two equal-momentum vectors of 15.0 kg · m/s in magnitude is 72.0° when placed tail to tail. What is the magnitude of the resultant?
Solve the triangles with the given parts.a = 0.208, c = 0.697, B = 165.4°
Find the required horizontal and vertical components of the given vectors. At one point, the Pioneer space probe was entering the gravitational field of Jupiter at an angle of 2.55° below the horizontal with a velocity of 18,550 mi/h. What were the components of its velocity?
Find the indicated vector sums and differences with the given vectors by means of diagrams.E − B A B C D E
What is the magnitude of a velocity vector that makes an angle of 18.0° with its horizontal component of 420 mi/h?
A nut is in the shape of a regular hexagon (six sides). If each side is 9.53 mm, what opening on a wrench is necessary to tighten the nut? See Fig. 9.78. Fig. 9.78 9.53 mm,
A Mars rover travels 569 m in a straight line and then stops to take a soil sample. It then changes direction and travels another 642 m where it takes another sample. If it must turn on a 47.2° corner to return to its starting point, what are the possible distances from its starting point?
Find the required horizontal and vertical components of the given vectors. Two upward forces are acting on a bolt. One force of 60.5 lb acts at an angle of 82.4° above the horizontal, and the other force of 37.2 lb acts at an angle of 50.5° below the first force. What is the total upward force on
A communications satellite is directly above the extension of a line between receiving towers A and B. It is determined from radio signals that the angle of elevation of the satellite from tower A is 89.2°, and the angle of elevation from tower B is 86.5°. See Fig. 9.66. If A and B are 1290 km
Solve the triangles with the given parts.a = 7.86, b = 2.45, C = 2.5°
In searching for a boat lost at sea, a Coast Guard cutter leaves a port and travels 75.0 mi due east. It then turns 65° north of east and travels another 75.0 mi, and finally turns another 65.0° toward the west and travels another 75.0 mi. What is its displacement from the port?
Find the required horizontal and vertical components of the given vectors. Vertical wind sheer in the lowest 100 m above the ground is of great importance to aircraft when taking off or landing. It is defined as the rate at which the wind velocity changes per meter above ground. If the vertical
Find the indicated vector sums and differences with the given vectors by means of diagrams.C − D A B C D E
The angle between two forces of 1700 N and 2500 N is 37° when placed tail to tail. What is the magnitude of the resultant force?
The apparent depth of an object submerged in water is less than its actual depth. A coin is actually 5.00 in. from an observer’s eye just above the surface, but it appears to be only 4.25 in. The real light ray from the coin makes an angle with the surface that is 8.1° greater than the angle the
A sign that weighs 275 lb hangs from the side of a building. The sign is supported by a cable angled at 45° from a rigid horizontal bar as shown in Fig. 9.47. Make a free-body diagram, and then find the tension T in the upper cable and the force F exerted on the horizontal bar. Fig.
A naval cruiser on maneuvers travels 54.0 km at 18.7° west of north, then turns and travels 64.5 km at 15.6° south of east, and finally turns to travel 72.4 km at 38.1° east of south. Find its displacement from its original position. See Fig. 9.31. Fig. 9.31 W- 54.0 km N s. 15.6° S 64.5
In order to move an ocean liner into the channel, three tugboats exert the forces shown in Fig. 9.30. What is the resultant of these forces? Fig.9.30 15.5° 22.2° 5500 Ib 6500 Ib 3500 Ib
A fire boat that travels 24.0 km/h in still water crosses a river to reach the opposite bank at a point directly opposite that from which it left. If the river flows at 5.0 km/h, what is the velocity of the boat while crossing?
In a baseball field, the four bases are at the vertices of a square 90.0 ft on a side. The pitching rubber is 60.5 ft from home plate. See Fig. 9.76. How far is it from the pitching rubber to first base? Fig. 9.76 1J09 90.0 ft
Find the indicated vector sums and differences with the given vectors by means of diagrams.A − B A B C D E
In widening a highway, it is necessary for a construction crew to cut into the bank along the highway. The present angle of elevation of the straight slope of the bank is 23.0°, and the new angle is to be 38.5°, leaving the top of the slope at its present position. If the slope of the present
Solve the triangles with the given parts.a = 186, B = 130.0°, c = 106
Find the total length of the path of the laser beam that is shown in Fig. 9.65. Fig. 9.65 6.25 cm 31.8° 108.3⁰ Reflectors
Find the indicated vector sums and differences with the given vectors by means of diagrams.2D + A A B C D E
Find the required horizontal and vertical components of the given vectors. A wheelbarrow is being pushed with a force of 80 lb directed along the handles, which are at an angle of 20° above the horizontal. What is the effective force for moving the wheelbarrow forward?
A plane leaves an airport and travels 624 km due east. It then turns toward the north and travels another 326 km. It then turns again less than 180° and travels another 846 km directly back to the airport. Through what angles did it turn?
Add the given vectors by components. The displacement vectors in Fig. 9.29. 25.0° 22.3 km 62.6° 41.5 km 42.2° Fig. 9.29 ·X 51.6 km
A crowbar 1.5 m long is supported underneath 1.2 m from the end by a rock, with the other end under a boulder. If the crowbar is at an angle of 18° with the horizontal and a person pushes down, perpendicular to the crowbar, with a force of 240 N, what vertical force is applied to the boulder? See
Find the angle between the front legs and the back legs of the folding chair shown in Fig. 9.75. Fig. 9.75 21 in. 25 in. 19 in. —
Solve the triangles with the given parts.B = 40.6°, b = 7.00, c = 18.0
A scuba diver’s body is directed downstream at 75° to the bank of a river. If the diver swims at 25 m/min, and the water is moving at 5.0 m/min, what is the diver’s velocity?
An Amazon robot begins at point O and travels in a straight line across a warehouse floor to point A where it picks up some merchandise. It then turns a 35° corner and travels 32.5 m to point B where it drops off the merchandise. See Fig. 9.64. If the robot must now turn a 29.0° corner to return
Add the given vectors by components. The force vectors in Fig. 9.28. 302 lb 45.4° 53.0° 155 lb Fig. 9.28 212 lb 30.8°
When an airplane is landing at an 8250-ft runway, the angles of depression to the ends of the runway are 10.0° and 13.5°. How far is the plane from the near end of the runway?
Find the indicated vector sums and differences with the given vectors by means of diagrams.3C + E A B C D E
Solve the triangles with the given parts.b = 14.5, c = 13.0, C = 56.6°
The robot arm shown in Fig. 9.74 places packages on a conveyor belt. What is the distance x? Fig. 9.74 2.50 m 102.0⁰ X 1.75 m Belt
Find the required horizontal and vertical components of the given vectors. A person applies a force of 210 N perpendicular to a jack handle that is at an angle of 25° above the horizontal. What are the horizontal and vertical components of the force?
Find the indicated vector sums and differences with the given vectors by means of diagrams.A + 2C A B C D E
Find the required horizontal and vertical components of the given vectors. The tension in a rope attached to a boat is 55.0 lb. The rope is attached to the boat 12.0 ft below the level at which it is being drawn in. At the point where there are 36.0 ft of rope out, what force tends to bring the
Add the given vectors by components. The velocity vectors in Fig. 9.27. 62.8⁰ 86.5 mi/h 40.5° X 62.0 mi/hr Fig. 9.27
Solve the triangles with the given parts.A = 77.06°, a = 12.07, c = 5.104
Find the distance from Atlanta to Raleigh, North Carolina, from Fig. 9.63. Fig. 9.63 Memphis 330 mi 640 mi 136° Atlanta Raleigh
A mine shaft goes due west 75 m from the opening at an angle of 25° below the horizontal surface. It then becomes horizontal and turns 30° north of west and continues for another 45 m. What is the displacement of the end of the tunnel from the opening?
Add the given vectors by components. The displacement vectors in Fig. 9.26. 318 m 67.5⁰ 245 m/ -16.3⁰ Fig. 9.26 -X
Find the required horizontal and vertical components of the given vectors. Vehicles on either side of a canal are towing a barge in the canal. If one pulls with a force of 760 N at 18° with respect to a line in the center of the canal, at what angle should the other pull with a force of 820 N so
Solve the triangles with the given parts.b = 7607, c = 4053, B = 110.09°
A passenger on a cruise ship traveling due east at a speed of 32 km/h notes that the smoke from the ship’s funnels makes an angle of 15° with the ship’s wake. If the wind is from the southwest, find the speed of the wind.
In viewing an island from a ship, at a point 3.15 km from one end of the island, and 7.25 km from the other end, the island subtends an angle of 33.9°. What is the length of the island?
Find the indicated vector sums and differences with the given vectors by means of diagrams.B + 3E A B C D E
Find the tension T in the left guy wire attached to the top of the tower shown in Fig. 9.62. Fig. 9.62 105.6° 850 N 35.7°
As a satellite travels around Earth at an altitude of 22,320 mi, the magnitude of its linear velocity remains unchanged, but its direction changes continually, which means there is a change in velocity. Using a diagram based on Fig. 9.45, draw the difference in velocities (subtract the first
Use the law of sines to solve the given problems. Two ropes hold a 175-lb crate as shown in Fig. 9.61. Find the tensions T1 and T2 in the ropes. 42.0⁰ T₁ 175 Ib Crate Fig. 9.61 30.0° T₂
Find the indicated vector sums and differences with the given vectors by means of diagrams.B + E + A A B C D E
Solve the triangles with the given parts.A = 71.0°, B = 48.5°, c = 8.42
Find the required horizontal and vertical components of the given vectors. The end of a robot arm is 3.50 ft on a line 78.6° above the horizontal from the point where it does a weld. What are the components of the displacement from the end of the robot arm to the welding point?
Three circles of radii 24 in., 32 in., and 42 in. are externally tangent to each other (each is tangent to the other two). Find the largest angle of the triangle formed by joining their centers.
Add the given vectors by components.A = 64, θA = 126°B = 59, θB = 238°C = 32, θC = 72°
The Pentagon (headquarters of the U.S. Department of Defense) is the largest office building in the world. It is a regular pentagon (five sides), 921 ft on a side. Find the greatest straight-line distance from one point on the outside of the building to another outside point (the length of a
Find the indicated vector sums and differences with the given vectors by means of diagrams.2A + D + E A B C D E
Solve the triangles with the given parts.a = 22.8, B = 33.5°, C = 125.3°
As a nuclear submarine moves eastward, it travels 0.50 km in a straight line as it descends 0.30 km below the surface. It then turns southward and travels 0.90 km in a straight line while resurfacing. What is its displacement from its original position?
Find the required horizontal and vertical components of the given vectors. With the sun directly overhead, a plane is taking off at 125 km/h at an angle of 22.0° above the horizontal. How fast is the plane’s shadow moving along the runway?
Find the indicated vector sums and differences with the given vectors by means of diagrams.B + D + A A B C D E
An airplane leaves an airport traveling 385 mi/h on a course 27.3° east of due north. Fifteen minutes later, a second plane leaves the same airport traveling 455 mi/h on a course 19.4° west of due north. What is the distance between the two planes one hour after the first plane departed?
Add the given vectors by components.U = 0.364, θU = 175.7°V = 0.596, θV = 319.5°W = 0.129, θW = 100.6°
In navigation, one method of expressing bearing is to give a single angle measured clockwise from due north. A radar station notes the bearing of two planes, one 15.5 km away on a bearing of 22.0°, and the other 12.0 km away on a bearing of 180.0°. Find the displacement of the second plane from
In an aerial photo of a triangular field, the longest side is 86.0 cm, the shortest side is 52.5 cm, and the largest angle is 82.0°. The scale is 1 cm = 2 m. Find the actual length of the third side of the field.
Solve the triangles with the given parts.A = 132.0°, b = 0.750, C = 32.0°
On a mountain trek, a pack mule becomes obstinate and refuses to move. One man pulls on a rope attached to the mule’s harness at 15° to the left of straight ahead with a force of 320 N, and a second man pulls with a force of 280 N at 12° to the right. With what force does the mule resist if the
Find the required horizontal and vertical components of the given vectors. A car traveling at 25 mi/h hits a stone wall at an angle of 65° with the wall. What is the component of the car’s velocity that is perpendicular to the wall?
Use the law of cosines to solve the given problems. Find the length of the chord intercepted by a central angle of 54.2° in a circle or radius 18.0 cm.
Add the given vectors by components.R = 630,θR = 189.6°F = 176, θF = 320.1°T = 324, θT = 75.4°
Use the law of sines to solve the given problems. The loading ramp at a delivery service is 12.5 ft long and makes a 18.0° angle with the horizontal. If it is replaced with a ramp 22.5 ft long, what angle does the new ramp make with the horizontal?
Find the indicated vector sums and differences with the given vectors by means of diagrams.A + C + E A B C D E
Solve the triangles with the given parts.A = 48.0°, B = 68.0°, a = 145
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