Resource Quiz 3 - schroeder(cs39963 Resource 3 Trigonometry...

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schroeder (cs39963) – Resource 3: Trigonometry and Vectors – balasubramanya – (1401310) 1 This print-out should have 30 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The unit vectors i , j , k are the same as the unit vectors x , y , and z . 001 10.0 points When an airplane leaves the runway, its angle of climb is 14 and its speed is 308 feet per second. How long will it take the plane to climb to an altitude of 10326 feet? Correct answer: 138 . 582 sec. Explanation: h d = v t θ sin θ = h v t t = h v sin θ t = 10326 308 sin 14 138 . 582 sec 002 10.0 points A boat is pulled in by means of a winch lo- cated on a dock 10 feet above the deck of the boat. Let θ be the angle of elevation from the boat to the winch and let s be the length of the rope from the winch to the boat. θ s 10 ft Find θ when s = 43 ft. Correct answer: 0 . 234707 rad. Explanation: From the figure, sin θ = 10 s θ = arcsin parenleftbigg 10 43 parenrightbigg 0 . 234707 003 10.0 points From an h = 96 feet observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression of the boat is θ = 3 . θ h How far (in feet) is the boat from the shore- line? Correct answer: 1831 . 79 feet. Explanation: The angle of depression from the tower to the boat is the same as the angle of inclination from the boat to the tower (see the picture below). θ θ h x Now, by the properties of right triangle, we obtain: tan θ = h x x = h tan θ = = 96 feet tan 3 1831 . 79 feet . 004 10.0 points A passenger in an airplane flying at 30000 ft sees two towns directly to the left of the airplane. The angles of depression to the towns are 36 and 74 .
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schroeder (cs39963) – Resource 3: Trigonometry and Vectors – balasubramanya – (1401310) 2 h + Town 1 Town 2 θ 2 θ 1 How far apart are the towns? Correct answer: 32689 . 1 ft. Explanation: θ 1 a h tan 36 = 30000 a a = 30000 tan 36 θ 2 a h tan 74 = 30000 b b = 30000 tan 74 dist = a b = 30000 tan 36 30000 tan 74 = 32689 . 1 ft . 005 10.0 points A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (5 . 2 m , 9 . 6 m), what is the distance of the fly from the corner of the room? Correct answer: 10 . 9179 m. Explanation: Let : x = 5 . 2 m and y = 9 . 6 m . Using the Pythagorean Theorem, d = radicalBig (∆ x ) 2 + (∆ y ) 2 = radicalBig (5 . 2 m) 2 + (9 . 6 m) 2 = 10 . 9179 m . 006 10.0 points Which of acceleration, age, speed, tempera- ture, and velocity are vector quantities? 1. All are vectors. 2. Acceleterion, speed, velocity 3. All are scalars. 4. Speed and temperature 5. Acceleration, age, speed 6. Age, speed, temperature 7. Acceleration, age, speed, temperature 8. Acceleration, speed, temperature 9. Age and temperature 10. Acceleration and velocity correct Explanation: Age is a measure of how long something exists; a scalar quantity.
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