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2415-2-review

# 2415-2-review - CalIII:Test2Review Name MULTIPLECHOICE. 13...

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Cal III: Test 2 Review Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate the function. 1) r (t) = (4t 2 - 6) i + 1 18 t 3 j A) r ʹ (t) = 1 6 t 2 i + (8t) j B) r ʹ (t) = (8t) i + 1 6 t 2 j C) r ʹ (t) = (8) i + 1 3 t j D) r ʹ (t) = (8t) i - 1 6 t 2 j 1) If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. 2) Find the velocity vector. r (t) = (cot t) i + (csc t) j A) v = (csc 2 t) i + (cot t csc t) j B) v = (sec 2 t) i + (tan t sec t) j C) v = ( - sec 2 t) i - (tan t sec t) j D) v = ( - csc 2 t) i - (cot t csc t) j 2) 3) Find the velocity vector. r (t) = (2t 2 - 14) i + 1 18 t 3 j A) v = 1 6 t 2 i + (4t) j B) v = (4) i + 1 3 t j C) v = (4t) i + 1 6 t 2 j D) v = (4t) i - 1 6 t 2 j 3) 4) Find the acceleration vector. r (t) = (6 ln(4t)) i + (3t 3 ) j A) a = 6 t i + 9t j B) a = - 3 2 t - 2 i + 18t j C) a = 6 t 2 t - 2 i + 18t j D) a = - 6 t 2 i + 18t j 4) Solve the initial value problem. 5) Differential Equation: d r dt = (cos t) i + (4t 3 + 3) j Initial Condition: r (0) = - 4 j A) r (t) = ( - sin t) i + (12t 2 - 4) j B) r (t) = (sin t) i + (t 4 ) j C) r (t) = (sin t) i + (t 4 - 4) j D) r (t) = (sin t) i + (t 4 + 3t - 4) j 5) 6) Differential Equation: d r dt = 9 2 (t + 3) 7/2 i + e t j Initial Condition: r (0) = 0 A) r (t) = [(t + 3) 11/2 - 3 11/2 ] i + (e t - 1) j B) r (t) = (t + 3) 9/2 i + e t j C) r (t) = [(t + 3) 9/2 - 3 9/2 ] i + (e t - 1) j D) r (t) = [(t + 3) 9/2 + 3 9/2 ] i + (e t + 1) j 6) 1

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Solve the problem. Unless stated otherwise, assume that the projectile flight is ideal, that the launch angle is measured from the horizontal, and that the projectile is launched from the origin over a horizontal surface 7) An ideal projectile is launched from the origin at an angle of α radians to the horizontal and an initial speed of 100 ft/sec. Find the position function r (t) for this projectile. A) r (t) = (100t sin α ) i + (100t cos α - 16t 2 ) j B) r (t) = (100t cos α ) i + (100t sin α - 16t 2 ) j C) r (t) = (100t cos α - 32t 2 ) i + (100t sin α ) j D) r (t) = (100t sin α - 16t 2 ) i + (100t cos α ) j 7)
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2415-2-review - CalIII:Test2Review Name MULTIPLECHOICE. 13...

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