The moon orbits the Earth in an approximately circular path. The position of the

Question

The moon orbits the Earth in an approximately circular path. The position of the moon as a function of time is given by: x(t) = r cos (omega t) Y(t) = r sin (omega t) where r = 3.84 times 10^8 m and omega = 2.46 times 10^-6 radians/s. What is the average velocity of the moon measured over the interval from t = 0 to t = 8.72 days?. Find its magnitude and direction, given as an angle measured counterclockwise from the positive x-axis. magnitude m/s direction degree counterclockwise from the + x-axis. A particle has a positive function r vector (t) = (cos (5.0t)i + sin(5.0t)j + tk) m, Where the arguments of the and (Express your answers in vector form. Use the following as necessary t, Assume r is in seconds, v vector in m/s, and a vector is in m/s^2. Do not include units in your answers.) (a) What is the velocity vector? v vector (t) = (b) What is the acceleration vector? a vector (t) =

Explanation / Answer

so the angle moved is wt = 2.46 * 10 ^ -6 * 24 * 60 * 60 * 8.72 = 1.853 radians

displacement = 2 * R * sin(theta/2)
= 2 * 3.84 * 10 ^ 8 * sin( 1.853/2) = 6.141 * 10 ^ 8 metres

and v = s/t = 6.141 * 10 ^ 8 / ( 8.72*24*60*60) = 815.096 m/s

angle = pi/2 + Q / 2 = 2.497 radians from the +x direction.

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