During the blizzard of ’88, a rancher was forced to drop hay baled from an airpl
ID: 3279260 • Letter: D
Question
During the blizzard of ’88, a rancher was forced to drop hay baled from an airplane to feed her cattle. The plane flew at 160 km/hr at a height of 80 m in a path that crossed directly over the cattle. She wanted to drop the hay close enough to the cattle to minimize the distance they had to walk through the very deep snow to get the food, but not so close as to possibly crush them. She decided to drop the bales 30 m behind the cattle. You can ignore air resistance in your calculations.
(Draw all figures with proper labels and list all Fundamental Laws (i.e Newton's Laws), Fundamental Principles (i.e Conservation of Momentum), or Mathematical Rules (i.e Chain Rule) and where they were applied).
1.) How far from the cattle should the plane be when she pushes the bale out?
2.) What is the largest time error she could make without hitting a cow?
Explanation / Answer
The height of the aerplane,h = 80 m
The velocity of the plane,u = 160 km/h = 44.44 m/s
1. The horizontal distance travelled by bales from airplane,
R = u(2h/g)^1/2
R = 44.44(2*80/9.8)^1/2
R = 179.56 m
Now, the bales of hay to land 30 m behind the cattle, so
R + 30 = 149.56 =u(2h/g)^1/2
h = (209.56)^2*4.9/1974.9
h = 108.96 m
therefore, to land the hay 30 m just behind the cattle the plane should be project
the hay at a height 108.96 m from the gronud
2. The largest time error that can be made while pushing the bales that not to be hit
the cattle, t = (2h/g)^1/2
t = (2*108.96/9.8)^1/2
t = 4.72 sec
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