In a relief operation mission involving a helicopter h distance above the ground traveling with a horizontal velocity vx. What should be the expression for the horizontal distance dx at which you release the relief package so that it will arrive to the survivors at the right place? (Neglect the effect of air resistance)

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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In a relief operation mission involving a helicopter h distance above the ground traveling with a horizontal velocity vx. What should be the expression for the horizontal distance dx at which you release the relief package so that it will arrive to the survivors at the right place? (Neglect the effect of air resistance)

Solution

To determine this, we must first derive the time it takes for the relief package to reach the survivors. We use this equation

-h = vinitial-yt + (1/2)ay ________

If we just drop the package from the helicopter, the equation above becomes

________ = ________ + (1/2)ay ________

Substituting ay = -g then simplifying results to

t = sqrt( ________ / ________ )

which is the time it takes for the object to reach the ground.

Since the package will just travel at a constant velocity in the x-axis, thus

dx = vxt

Substituting the time taken by the package to reach to ground results to:

dx = ( ________ )( sqrt ( ________ / ________ ) )

which is the expression for the horizontal distance at which you should drop the package.

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