If a helicopter flies linearly in the upward direction from a point A on the earth stays in the air at the same position for a long time and then linearly comes down , will it land at the same point A or at a different point since the earth is rotating ?

  • $\begingroup$ If you are in a plane and you throw a ball out of the window, the trajectory followed by the ball will be the same as a parabola for someone that is in the ground watching the whole thing. If you are in the plane, since the plane is moving, you will only be able to watch the body going on a straight line to the ground. $\endgroup$ – user249212 Dec 28 '19 at 10:37
  • $\begingroup$ You can think of this way to answer your question. While the helicopter is in the ground it will be following the rotation of the earth, with some velocity and when it goes to the air he continues to follow the earth rotation so I guess that it will land on the same point (in ideal conditions, because it will require quite precision to do that in practise) $\endgroup$ – user249212 Dec 28 '19 at 10:39
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    $\begingroup$ Well what do you think and why $\endgroup$ – Bob D Dec 28 '19 at 11:24
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    $\begingroup$ see en.wikipedia.org/wiki/Coriolis_force $\endgroup$ – Adrian Howard Dec 28 '19 at 11:28
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    $\begingroup$ Does this answer your question? Can a hovering helicopter travel half the globe in 12 hours? $\endgroup$ – Kyle Kanos Dec 28 '19 at 12:39

If it stays up for a long time it will land on a different spot, because the forward velocity required to stay above the initial spot is $v_{\perp}=\omega \cdot r$ (angular velocity times distance from the center), but the higher you go, the larger the $r$, so your initial $v_{\perp}$ will be smaller than the $v_{\perp}$ required at a larger $r$.

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  • $\begingroup$ So in case we have a satellite as they remain in space for a very long time , will they also revolve aoround the sun as earth does ? $\endgroup$ – Sameer nilkhan Dec 28 '19 at 11:15
  • $\begingroup$ @Sameernilkhan I don't think you understand the condition for revolution around a body. There needs to be a centripetal force for the body to orbit something. $\endgroup$ – Sam Dec 28 '19 at 13:16

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