Question:

Can anyone help me solve this physics question?

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At a particular instant, a stationary observer on the ground sees a package falling from a moving airplane with a speed V(observer) at an angle theta to the vertical. To the pilot flying horizontally at a constant speed relative to the ground the package appears to be falling vertically with a speed V(pilot) at that same instant. What is the speed of the pilot relative to the ground in terms of the given quantities?

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  1. if we are ignoring the effects of air friction, the horizontal motion of the package will equal the horizontal motion of the plane at the moment the package was released.

    the total velocity according to the observer consists of this horizontal component plus a vertical component due to the acceleration of gravity

    the horizontal component of the package observed by the observer will be v(o) sin(theta)  (it is sin(theta) because the angle is measured with respect to the vertical)

    since the horizontal motion of the plane and package are the same, the speed of the plane is then v(0) sin(theta)

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