SECTION 9.4 Vectors 649 89. Static Equilibrium A weight of 1000 pounds is suspended from two cables, as shown in the figure.What are the tensions in the two cables? 258 408 1000 pounds 90. Static Equilibrium A weight of 800 pounds is suspended from two cables, as shown in the figure.What are the tensions in the two cables? 358 508 800 pounds 91. Static Equilibrium A tightrope walker located at a certain point deflects the rope as indicated in the figure. If the weight of the tightrope walker is 150 pounds, how much tension is in each part of the rope? 150 pounds 3.78 4.28 92. Static Equilibrium Repeat Problem 91 if the angle on the left is ° 3.8 , the angle on the right is ° 2.6 , and the weight of the tightrope walker is 135 pounds. 93. Static Friction A 20-pound box sits at rest on a horizontal surface, and there is friction between the box and the surface. One side of the surface is raised slowly to create a ramp. The friction force f opposes the direction of motion and is proportional to the normal force FN exerted by the surface on the box.The proportionality constant is called the coefficient of friction, μ. When the angle of the ramp, θ, reaches ° 20 , the box begins to slide. Find the value of μ to two decimal places. 20 pounds u FN f 80. Finding the Actual Speed and Direction of an Aircraft An Airbus A320 jet maintains a constant airspeed of 500 mph headed due west. The jet stream is 100 mph in the southeasterly direction. (a) Express the velocity va of the A320 relative to the air and the velocity vw of the jet stream in terms of i and j. (b) Find the velocity of the A320 relative to the ground. (c) Find the actual speed and direction of the A320 relative to the ground. 81. Ground Speed and Direction of an Airplane An airplane has an airspeed of 500 kilometers per hour (km/h) bearing ° N45 E. The wind velocity is 60 km/h in the direction ° N30 W. Find the resultant vector representing the path of the plane relative to the ground.What is the groundspeed of the plane? What is its direction? 82. Ground Speed and Direction of an Airplane An airplane has an airspeed of 600 km/h bearing ° S30 E. The wind velocity is 40 km/h in the direction ° S45 E. Find the resultant vector representing the path of the plane relative to the ground. What is the groundspeed of the plane? What is its direction? 83. Weight of a Boat A force of magnitude 700 pounds is required to hold a boat and its trailer in place on a ramp whose incline is ° 10 to the horizontal. What is the combined weight of the boat and its trailer? 84. Weight of a Car A force of magnitude 1200 pounds is required to prevent a car from rolling down a hill whose incline is ° 15 to the horizontal.What is the weight of the car? 85. Correct Direction for Crossing a River A river has a constant current of 3 km/h. At what angle to a boat dock should a motorboat capable of maintaining a constant speed of 20 km/h be headed in order to reach a point directly opposite the dock? If the river is 1 2 kilometer wide, how long will it take to cross? 86. Finding the Correct Compass Heading The pilot of an aircraft wishes to head directly east but is faced with a wind speed of 40 mph from the northwest. If the pilot maintains an airspeed of 250 mph, what compass heading should be maintained to head directly east? What is the actual speed of the aircraft? 87. Charting a Course A helicopter pilot needs to travel to a regional airport 25 miles away. She flies at an actual heading of ° N16.26 E with an airspeed of 120 mph, and there is a wind blowing directly east at 20 mph. (a) Determine the compass heading that the pilot needs to reach her destination. (b) How long will it take her to reach her destination? Round to the nearest minute. 88. Crossing a River A captain needs to pilot a boat across a river that is 2 km wide. The current in the river is 2 km/h and the speed of the boat in still water is 10 km/h. The desired landing point on the other side is 1 km upstream. (a) Find the direction that the captain should take. (b) How long will the trip take? Current Boat Direction of boat due to current
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