The earth's radius is 6.37 × 10 6 m; it rotates once every 24 hours.The angular speed is ω = 7.3 × 10 − 5 r a d / sThe speed of the point on the equator is v = 460 msWhat is the speed of a point on the earth's surface located at 2/5 of the length of the arc between the equator and the pole, measured from equator?

Question

The earth&#039;s radius is   6.37  ×      10    6       m; it rotates once every 24 hours.The angular speed is   ω  =  7.3  ×      10          −      5           r  a  d      /    sThe speed of the point on the equator is v = 460 msWhat is the speed of a point on the earth&#039;s surface located at 2/5 of the length of the arc between the equator and the pole, measured from equator?

Theresa Sims · Accepted Answer

The radius of the Earth,The angular speed at the equator,The speed of the point on the equator,  R  =  6.37  ×      10    6       m    ω  =  7.3  ×      10          −      5           r  a  d      /    s    v  =  460     m      /    sThe angle from equator to pole,The angle from equator to 2/5 length of the arc,      θ    0    =      90          ∘          θ  =  (      2    5    )      90          ∘          =      36          ∘      The radius at 2/5 length of the arc between equator and the pole,  r  =  R  cos  ⁡  θ    r  =  (  6.37  ×      10    6       m  )  cos  ⁡      36          ∘          =  5.15  ×      10          6           mThe speed at 2/5 length of the arc between equator and the pole,  v  =  r  ωThe speed at 2/5 length of the arc between equator and the pole is 375.95 m/s.  v  =  (  5.15  ×      10    6       m  )  (  7.3  ×      10          −      5           r  a  d      /    s  )    =  375.95     m      /    s

what is the speed of a point on the earth's surface located at 2/5 of the length of the arc between the equator and the pole, measured from equator?

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