Question

To take the time derivate of vectors that are defined in terms of fixed and moving coordinate systems. Students should be able to use the time derivative of vectors to calculate the linear and angular acceleration of points on a body.

A satellite floating in space is subjected to three angular velocities, ωA, ωZ and ωy. At the instant shown ωA is directed along the antenna ending at Aand has a magnitude of 5.50 rad/s , ωZ has a magnitude of 7.70 rad/s and is always directed along the Z axis, ωy has a magnitude of 8.50 rad/s and is always directed along the y axis. Three angular accelerations act on the satellite, ω˙A=0.250 rad/s2, ω˙Z=0.110 rad/s2, and ω˙y=0.170 rad/s2, which each act in the same direction as their respective angular velocities. Point Ais located at (−1.80, 1.70, 0.670). The dimensions a, b, and c have lengths of 1.50 m, 1.90 m, and 0.950 m, respectively. The coordinate axes XYZ are fixed and share the origin O with the rotating axes xyz, which are coincident at the instant shown.

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Find the velocity of B with respect to O in component form. Express your answers, separated by commas, to three significant figures in m/s. View Available Hint(s) vB= vB= 5.766,18.274,17.321 i, j, k m/s SubmitPrevious Answers Incorrect; Try Again; 2 attempts remaining Part B - Acceleration of B Calculate the acceleration of B at the instant shown. Express your answer in component form. Express your answers, separated by commas, to three significant figures in m/s2. View Available Hint(s) aB= aB= nothing i, j, k m/s2 Submit Part C - Acceleration of A Calculate the acceleration of A at the instant shown. Give your answer in component form. Express your answers, separated by commas, to three significant figures in m/s2. View Available Hint(s) aA= aA= nothing i, j, k m/s2 Submit Provide Feedback Next

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Answer 1

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