# Airplane Dropping a Package Relative Motion

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1. Sep 27, 2015

### DanielleG

1. The problem statement, all variables and given/known data

A Red Cross airplane is travelling horizontally east at velocity v_0 = 80.0 m/s and height h = 350 m above the ground. The plane carries emergency supplies for a village inaccessible by road. The plane will drop the package (without a parachute) into a pile of soft hay prepared on the ground to cushion the impact. The pilot looks at her instruments and notices the plane is a horizontal distance $d = 2900$ m from the hay pile. A time t_1 later, the copilot pushes the package out of the plane, with a westward horizontal velocity v_s = 3 m/s relative to the plane. It lands exactly on the hay pile. From the instant the package leaves the plane, how much time elapses till it hits the hay pile? (Neglect air resistance.)

2. Relevant equations

$$y_f=y_i+v_yt-\frac{1}{2}gt^2$$

Where $$g=9.8\frac{m}{s^2}$$, y_f is the final height, and y_i, the initial height

3. The attempt at a solution

I have drawn a diagram (see attached file) but I am unsure of where to start. If anyone had any advice for where to begin, that would be great!

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2. Sep 27, 2015