Please can I have the correct solution to this problem in a step by step form. Thanks very much. Question 4(a) An object is moving with position vector r(t) = cos(@t)i+sin(cot)j + at³k.(i)Determine the velocity and acceleration vector of the object.(ii)If = rads s¹ and a = 2 m s² determine the position and velocity ofthe object at 1 = 3 s.

Given :position vector :r(t)=cos(ωt)i+sin(ωt)j+αt2kω=π and α=2 and t=3

Answered: Question 4 (a) An object is moving with…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.7: Applied Problems

Problem 68E

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Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The first gear in a single-stage gear train has 42 teeth and an angular velocity of 2 revolutions per second. The second gear has 7 teeth. Find the angular velocity of the second gear.
Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The second gear in a single-stage gear train has 6 teeth and an angular velocity of 90 revolutions per minute. The first gear has 54 teeth. Find the angular velocity of the first gear.

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Question 4 (a) An object is moving with position vector r(t) = cos(cot)i+sin(at)j + at³k. (1) Determine the velocity and acceleration vector of the object. (ii) If = rads s¹ and a = 2 m s² determine the position and velocity of the object at 1 = 3 s.