How far short of the target should the plane drop the target?

A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 130 m above the glacier at a speed of 114 m/s. How far short of the target should it drop the package?How far short of the target should the plane drop the target?d = 130m (vertical)

v = 114 m/s (horizontal)



First of all we need to find the time, which is the same both horizontally and vertically. We use a kinematics equation (for vertical only, so vo is 0)



d = vot + 1/2 at^2

t^2 = 2d / a

t = sqrt (2d / a)



t = 5.2s



Now we have the time, we need to find the horizontal distance. We also have vo (horizontal) which we simply plug in to this equation:



v = d / t

d = vt

d = (114)(5.2)



d = 592.8 m short of the targetHow far short of the target should the plane drop the target?The time it takes to fall ( not including air friction ) is



t= sqrt ( 2 X distance of fall )/ 9.8 )) = 5.15 sec



Traveling at 114 m/s you'd have to release the package



114 X 5.15 = 587 m before the targetHow far short of the target should the plane drop the target?Have you even tried this? You lazy thing.



Time taken to fall vertically = time taken to travel horizontally.



sqrt(150*2/9.8) = x/114



Rearrange to find x.