Delivering a Package by Air (Project Time Motion) help

[Kalie]

Delivering a Package by Air (Project Time Motion)...help

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
Find the initial velocity of the package, v0, with respect to the ground.
Express the initial velocity of the package in terms of given quantities, v0,v1, h, and the magnitude of the acceleration due to gravity g, using x^ and y^ for the unit vectors in the x and y directions.

I figured the initial velocity of the package in the plane's frame of reference

vp=-v1x^

Velocity of the plane with respect to the ground

The frame of reference of the plane is moving with velocity +v0x^

I don't know what to do from there...
As you can tell I really don't get project time motion...

 

[andrevdh]

The "common" way of dealing with relative velocities is using subscripts:

$$v_{pg} = v_{pa} + v_{ag}$$

this indicates that the (horizontal) velocity of the package relative to the ground is given by the sum of the velocity of the package relative to the airplane, v1, and the velocity of the airplane relative to the ground, v0.

Since the velocity of the package is in the opposite direction we get

$$v_{pg} = v0 - v1$$

which will be a "positive" velocity in the sense that the package will have a "reduced" velocity in the direction of the motion of the airplane since it was thrown out towards the rear of the plane.