You are working as an assistant to an air-traffic controller at the local airport, from which small airplanes take off and land. Your job is to make sure that airplanes are not closer to each other than a minimum safe separation distance of 2.00 km. You observe two small aircraft on your radar screen, out over the ocean surface. The first is at altitude 800 m above the surface, horizontal distance 19.2 km. and 25.0° south of west. The second aircraft is at altitude 1 100 m, horizontal distance 17.6 km, and 20.0° south of west. Your supervisor is concerned that the two aircraft are too close together and asks for a separatism distance for the two airplanes. (Place the x axis west, the y axis south, and the z axis vertical.)
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Chapter 3 Solutions
Physics for Scientists and Engineers
- A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with three axes along three edges of the room, the fly changes its position from point b(4.0 m, 1.5 m, 2.5 m) to point e(1.0 m, 4.5 m, 0.5 m). Find the scalar components of the fly’s displacement vector and express its displacement vector in vector component form. What is its magnitude?arrow_forwardA radar station sends a signal to a ship which is located a distance 14.0 kilometers from the station at bearing 136° clockwise from the north. At the same moment, a helicopter is at a horizontal range of 19.6 kilometers, at bearing 152° clockwise from the north, with an elevation of 2.58 kilometers. Let east be the î direction, north be the ĵ direction, and up be the direction. (A) What is the displacement vector (in km) from the helicopter to the ship? (Express your answer in vector form. Do not include units in your answer.) (B) What is the distance (in km) between the helicopter and ship? (C) The ship begins to sink at a rate of 5.40 m/s. Write the position vector (in km) of the ship relative to the helicopter as a function of time as the ship sinks. Assume that the helicopter remains hovering at its initial position and that the sinking rate remains the same even after the ship sinks under the surface. (Use the following as necessary: t. Do not include units in your…arrow_forwardWhat is the magnitude of a→×(b→×a→) if there is an angle φ = 23.0° between the directions of a→ and b→? Assume a = 7.9 and b = 5.1.arrow_forward
- An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.6 km, but when the snow clears, he discovers that he actually traveled 7.8 km at 50° north of due east. (a) How far and (b) in what direction must he now travel to reach base camp?arrow_forwardA plane leaves Denver and travels 239 miles bearing N77 degrees W, then makes a course correction and travels N33 degrees W for 95 miles. How many miles north of Denver did they travel (round to two decimal places)?arrow_forwardA. downward and parabolic B. downward and circular C. upward, along a straight line D. upward and circular E. upward and parabolicarrow_forward
- An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.2 km, but when the snow clears, he discovers that he actually traveled 8.1 km at 45o north of due east. (a) How far and (b) in what direction (south of due west) must he now travel to reach base camp?arrow_forwardVector A : Magnitude: 1.569 N Angle: 0 degrees x-component : 1.569 N y-component : 0 N Vector B : Magnitude: 0.4801 N Angle: 80 degrees x-component: .0834 N y-component: .4728 N Draw a diagram and use the triangle method to find R1, by adding the vectors A and B.arrow_forwardTwo aircraft approaching an aircraft carrier are detected by radar. The first aircraft is at a horizontal distance of 34.3 km in the direction 42.0 north of east and has an altitude of 2.40 km. The second aircraft, at half this altitude, is at a horizontal distance of 42.6 km in the direction 37.0 north of east. What is the distance separating the two aircraft? Hint: Use a coordinate system with the x axis pointing east, the y axis pointing north, and the z axis in the vertical direction.arrow_forward
- The displacement vectors 42.0 cm at 15.0 and 23.0 cm at 65.0 both start from the origin and form two sides of a parallelogram. Both angles are measured counterclockwise from the x axis. (a) Find the area of the parallelogram. (b) Find the length of its longer diagonal.arrow_forwardA vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y component is negative. (c) The x component is negative, and the y component is positive. (d) Both components are negative. (e) More than one answer is possible.arrow_forwardA surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, he walks x = 1.00 102 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline lo the tree is = 35.0 (Fig. P1.53). How wide is the river? Figure P1.53arrow_forward
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