Package by Air (project time motion)

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SUMMARY

The discussion focuses on the physics of projectile motion as it relates to delivering a package from an airplane to a small island. The key equations derived include the horizontal distance formula D = (v0 - v1) * sqrt(2h/g) for determining when to release the package. The time of flight is calculated using t = sqrt(2h/g), where h is the altitude and g is the acceleration due to gravity. The velocity vector of the package upon impact with the ground is also a critical point of analysis.

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  • Knowledge of vector components in physics
  • Basic grasp of gravitational acceleration (g)
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Kalie
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A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed at an altitude . The package is ejected horizontally in the negative x direction with speed relative to the plane. Assume is v1 less than v0. The positive x and y directions are defined in the figure.

|0000(plane)--->v0
|
|h
|
|__________0000(island)
D

A. If the package were to land right on the island, at what horizontal distance from the plane to the island should the package be released?
B. What is the horizontal distance from the plane to the island when the package hits the ground?
C. Find the velocity vector of the package when it hits the ground.

I found that v0, with respect to the ground is v0x^-v1x^
and that t= sqrt((2h)/g)

I don't know what to do from there...

As you can tell I really don't get project time motion...
 
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I found part A D=(v0-v1)*sgrt(2h/g)
 
never mind I found it out :) i am really stupid...
 

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