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A radar station sends a signal to a ship which is located a distance 13.0 kilometers from the station at bearing 136° clocKwise from the north. At the same moment, a helicopter horizontal range of 19.6 kilometers, at bearing 155° clockwise from the north, with an elevation of 2.60 kilometers. Let east be the î direction, north be the j direction, and up be the k 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.)

A radar station sends a signal to a ship which is located a distance 13.0 kilometers from the station at bearing 136° clocKwise from the north. At the same moment, a helicopter horizontal range of 19.6 kilometers, at bearing 155° clockwise from the north, with an elevation of 2.60 kilometers. Let east be the î direction, north be the j direction, and up be the k 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.)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A radar station sends a signal to a ship which is located a distance 13.0 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 155° clockwise from the north, with an elevation of 2.60 kilometers. Let east be the î direction, north be the ĵ direction, and up be the k 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.) D = (0.75i + 8.41j + 2.60k Draw a sketch of the situation on the xy-axis, with the station at the origin, and write each position vector in unit-vector notation. Note that the helicopter will have an additional component in the +k-direction. Find S - H, the difference in the position vectors of the ship and helicopter. Be careful with your angles when you calculate components. Notice that for both position vectors, the x-components are positive and the y-components are negative. ) km (b) What is the distance (in km) between the helicopter and ship? 8.83 km (c) What If? The ship begins to sink at a rate of 5.30 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 answer.) D(t) î + ĵ + 2.60 + 19.1t When the ship begins to sink, its position in the k-direction changes at a rate of 5.30 m/s. Use the result from part (a), with the displacement vector in the k-direction modified accordingly as a function of time. Be sure your distance units are consistent. k) km (3 (d) Evaluate the position of the ship relative to the helicopter (in km) after 2.00 h. (Express your answer in vector form. Do not include units in your answer.) D(t) = ( 0.75i + 8.41j + 40.8k Use the result from part (c), with t = 2.00 h 7200 s. km
Transcribed Image Text:A radar station sends a signal to a ship which is located a distance 13.0 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 155° clockwise from the north, with an elevation of 2.60 kilometers. Let east be the î direction, north be the ĵ direction, and up be the k 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.) D = (0.75i + 8.41j + 2.60k Draw a sketch of the situation on the xy-axis, with the station at the origin, and write each position vector in unit-vector notation. Note that the helicopter will have an additional component in the +k-direction. Find S - H, the difference in the position vectors of the ship and helicopter. Be careful with your angles when you calculate components. Notice that for both position vectors, the x-components are positive and the y-components are negative. ) km (b) What is the distance (in km) between the helicopter and ship? 8.83 km (c) What If? The ship begins to sink at a rate of 5.30 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 answer.) D(t) î + ĵ + 2.60 + 19.1t When the ship begins to sink, its position in the k-direction changes at a rate of 5.30 m/s. Use the result from part (a), with the displacement vector in the k-direction modified accordingly as a function of time. Be sure your distance units are consistent. k) km (3 (d) Evaluate the position of the ship relative to the helicopter (in km) after 2.00 h. (Express your answer in vector form. Do not include units in your answer.) D(t) = ( 0.75i + 8.41j + 40.8k Use the result from part (c), with t = 2.00 h 7200 s. km
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