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**Unformatted text preview: **kuruvila (lk5992) – HW 1 – Opyrchal – (11113) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A basketball player is 6 ft 2 3 4 in tall. What is his height in centimeters? Correct answer: 189 . 865 cm. Explanation: We can convert to inches and then to cen- timeters: 6 ft 2 3 4 in = parenleftbigg 6 ft · 12 in 1 ft + 2 . 75 in parenrightbigg × 2 . 54 cm 1 in = 189 . 865 cm . 002 10.0 points For the given triangles, a = 11 . 1 m, b = 6 . 77 m, and α = 56 ◦ . a b α θ Find θ . Correct answer: 24 . 2921 ◦ . Explanation: Let the common side be x . a b x α θ In the triangle on the left, tan α = x a x = a tan α , and in the triangle on the right, sin θ = b x = b a tan α θ = arcsin parenleftbigg b a tan α parenrightbigg = arcsin bracketleftbigg 6 . 77 m (11 . 1 m) tan 56 ◦ bracketrightbigg = 24 . 2921 ◦ . 003 10.0 points A person walks 27 m East and then walks 40 m at an angle 25 ◦ North of East. What is the magnitude of the total dis- placement? Correct answer: 65 . 4723 m. Explanation: Let : R a = 27 m , R b = 40 m , and θ = 25 ◦ . The total displacement is the vector sum of the two displacements, so R x = R a + R b cos θ = 27 m + (40 m) cos25 ◦ = 63 . 2523 m and R y = R b sin θ...

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