Alternative Exercise 3.93 The Velocity of the Moon The velocity of the Moon rela

Question

Alternative Exercise 3.93 The Velocity of the Moon The velocity of the Moon relative to the center of the Earth can be approximated b v-(945m/s) sin (2.46 x 10-6 radians/s)t +cos (2.46 x 10 6radians sty where tis measured in seconds. The time required for the Moon to complete one orbit is 29.5 days.) Part A To approximate the instantaneous acceleration of the Moon at t 0, calculate the z and y components of the average acceleration between the times t 0 and t 0.100 days. Enter the x and y components of the average acceleration separated by comma. aa, ay m S Submit My Answers Give Up Incorrect; Try Again; 5 attempts remaining Part B To approximate the instantaneous acceleration of the Moon at t 0, calculate the z and y components of the average acceleration between the times t 0 and t 0.0100 days Enter the x and y components of the average acceleration separated by comma.

Explanation / Answer

A)

acceleration is given as

a = dv/dt = (945) (- (2.46 x 10-6) Cos(2.46 x 10-6)t x^ - (2.46 x 10-6) Sin(2.46 x 10-6)t y^))

ax = (945) (- (2.46 x 10-6) Cos(2.46 x 10-6)t

at t = 0 , ax = (945) (- (2.46 x 10-6) Cos(2.46 x 10-6)(0) = - (2.32 x 10-3) m/s2

at t = 0.1 days = 0.1 x 24 x 3600 = 8640 sec , ax = (945) (- (2.46 x 10-6) Cos(2.46 x 10-6)(8640) = - 0.00232 m/s2  

at t = 0 , ay = (945) (- (2.46 x 10-6) Sin(2.46 x 10-6)(0) = 0 m/s2

at t = 0.1 days = 0.1 x 24 x 3600 = 8640 sec , ay = (945) (- (2.46 x 10-6) Sin(2.46 x 10-6)(8640) = - 4.94 x 10-5 m/s2

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