A rancher will to drop hay bales from an airplane to feed the cattle. The plane

Question

A rancher will to drop hay bales from an airplane to feed the cattle. The plane flies horizontally at 160 km/hr and the bales are dropped from a height of 80 m above the flat range.
1. For the bales of hay to land 30 m behind the cattle where should the bales be pushed out of the airplane?
2.To not hit the cattle, what is the largest time error that can be made while pushing the bales out of the airplane? Ignore air resistance.
3. Redo the problem using simple numerical methods, such as Euler's Method. That is replace the derivative dx/dt with a difference ?x/?t.

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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