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At a particular instant, a stationary observer on the ground sees a package falling with speed v1 at an angle to the vertical. To a pilot flying horizontally at constant speed relative to the ground, the package appears to be falling vertically with a speed v2 at that instant. What is the speed of the pilot relative to the ground?

Ok, so the object falling relative to the observer has a different velocity then it does relative to the pilot. The y-component of the objects velocity will be identical for both reference frames, but the horizontal velocity is going to differ.

Ground speed is equal to the vector sum of Airspeed and Windspeed. If the pilot observes the package to be falling vertically, he must be approaching it from behind. Assuming the package was dropped vertically, the x-component of its velocity should reflect the windspeed?

So, the ground speed of the plane would be the sums of its constant velocity and the x-component of the objects velocity?

I am asking for some guidance with this questions, but not the answer, if someone could give me some hints.

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    $\begingroup$ Hi Kurt - it's much better if you can ask a question about the specific physics concept that is giving you trouble. Just asking for guidance isn't very specific. You're partway there already, since you're asking about determining the x component of the velocity, but perhaps you could on exactly what you're doing to try to figure that out that is not working? $\endgroup$
    – David Z
    May 10, 2012 at 4:34
  • $\begingroup$ I am having a difficult time with relative velocity. The x-compoents of the plane and the object must be equal, the plane however has no vertical velocity. So, perhaps the ground speed of the plane is the resultant velocity of the x component and y component of the object? I am having a hard time understanding how to think of the x and y components to arrive at a solution. $\endgroup$
    – Kurt
    May 10, 2012 at 5:30

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You already have all the points needed. I'll quote you:

The y-component of the objects velocity will be identical for both reference frames, but the horizontal velocity is going to differ.

and then you say

The x-compoents of the plane and the object must be equal, the plane however has no vertical velocity.

Now what you should do is to think of a famous theorem that connects the sum of the squares of the components of a vector to its magnitude. The answer will pop out then..!

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