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You are participating in a summer internship with the Coast Guard. You have been assigned the duty of determining the direction in which a Coast Guard speedboat should travel to intercept unidentified vessels. One day, the radar operator detects an unidentified vessel at a distance of 20.0 km from the radar installation in the direction 15.0° east of north. The vessel is traveling at 26.0 km/h on a course at 40.0° east of north. The Coast Guard wishes to send a speedboat, which travels at 50.0 km/h, to travel in a straight line from the radar installation to intercept and investigate the vessel, and asks you for the heading for the speedboat to take. Express the direction as a compass bearing with respect to due north.
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- A light plane attains an airspeed of 490 km/h. The pilot sets out for a destination 790 km due north but discovers that the plane must be headed 19.0° east of due north to fly there directly. The plane arrives in 2.00 h. What were the (a) magnitude and (b) direction of the wind velocity? Give the direction as an angle relative to due west, where north of west is a positive angle, and south of west is a negative angle. (a) Number i (b) Number Units Unitsarrow_forwardA diver explores a shallow reef off the coast of Belize. She initially swims d1 = 74.3 m north, makes a turn to the east and continues for d2 = 183.7 m, then follows a big grouper (a kind of fish) for d3 = 73.3 m in the direction θ = 43.9° north of east. Finally, she swims d4 = 193.4 m south.What is the straight-line distance between her initial and final positions in m?arrow_forwardA hiking girl needs to go 24.8 km straight North to get to base camp, instead the compass confuses her and she travels 11.904 km at a 6.1° deflection East from straight North. Then she realizes what she has done and so guesses an angle of 15.5° deflection West of straight North and then hikes 19.592 km. What is the magnitude of her displacement from where she is now located to base camp. (put your answer is standard units)arrow_forward
- A plane headed due south is traveling with an airspeed of 180 miles per hour. The wind currents are moving with constant speed in the direction 30°. If the ground speed of the plane is 90 miles per hour, what is its true course?arrow_forwardThe route followed by a hiker consists of three displacement vectors A,B ,c Cand . Vector A is along a measured trail and is 1550 m in a direction 25.0° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 41.0° east of south. Similarly, the direction of vector C is 10.0° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A+ B+ C = 0. Find the magnitudes of vector B and vector C .arrow_forwardAn 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 5.1 km, but when the snow clears, he discovers that he actually traveled 8.4 km at 46° north of due east. (a) How far and (b) in what direction (south of due west) must he now travel to reach base camp? (a) Number i 34.99 (b) Number 1.48 Units Units km ° (degrees)arrow_forward
- A hiker walks 2.5 miles in a direction 65° West of North, then 3.5 miles in a direction 40° South of West, then 1.5 miles due South. What must be the vector displacement of the hiker during the fourth part of the trip in order for the resultant to be 5.5 miles due West for the entire trip? Drawing a vector diagram or drawing individual vectors will help.arrow_forwardA boat radioed a distress call to a Coast Guard station. At the time of the call, a vector A from the station to the boat had a magnitude of 45.0 km and was directed 15.0 degrees east of north. A vector from the station to the point where the boat was later found is B= 30.0 km, 15.0 degrees north of east. (a) What are the components of the vector from the point where the distress call was made to point where the boat was found? In other words, what are the components of vector C = B - A? (b) How far did the boat travel from the point where the distress call was made to the point where the boat was found? In other words, what is the magnitude of vector C? Please show the complete and step by step soution. Thanks!arrow_forwardA drone is initially flying on a heading 40 degrees south of west at a speed of 284 knots. (A knot is about 1.15 miles per hour). A wind begins to blow due west at a speed of 50 knots. Find the resultant speed and direction of the drone.arrow_forward
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