Answer:
The plane should drop the package 632.8m away from the scientists
Explanation:
Given data
Our origins is the plane in the moment it drops the package
The positive vertical direction is upward
The positive horizontal direction is to the right
[tex]v_{ix}=140 m/s\\v_{iy}=0m/s\\y_{f}=-100m\\y_{i}=0m\\x_{i}=0m[/tex]
From equation of simple motion we know
[tex]y_{f}=y_{i}+v_{iy}t+(1/2)at^{2}\\ -100m=0+0+(0.5*-9.8m/s^{2}*t^{2} )\\t=\sqrt{(100/4.9)} \\t=4.52s[/tex]
From horizontal velocity:
[tex]v_{x}=\frac{x_{f}-x_{i}}{t}\\140m/s=\frac{x_{f}-0m}{4.52s}\\ x_{f}=140*4.52\\x_{f}=632.8m[/tex]
The plane should drop the package 632.8m away from the scientists
