Question

A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 100 m above the glacier at a speed of 140 m/s.How far short of the target should it drop the package?

Answer 1

The plane should drop the package 632.8m away from the scientists

Step-by-step 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

`v_(ix)=140 m/s\\v_(iy)=0m/s\\y_(f)=-100m\\y_(i)=0m\\x_(i)=0m`

From equation of simple motion we know

`y_(f)=y_(i)+v_(iy)t+(1/2)at^(2)\\ -100m=0+0+(0.5*-9.8m/s^(2)*t^(2) )\\t=√((100/4.9)) \\t=4.52s`

From horizontal velocity:

`v_(x)=(x_(f)-x_(i))/(t)\\140m/s=(x_(f)-0m)/(4.52s)\\ x_(f)=140*4.52\\x_(f)=632.8m`

The plane should drop the package 632.8m away from the scientists