A plane with a mass of 940kg is suddenly buffeted by a wind force directed to th

Question

A plane with a mass of 940kg is suddenly buffeted by a wind force directed to the right as shown. the wind force vs. time function is Fwind=5500-140e^3t. determine the sideward sliding distance if the plane is buffeted for 1.80 seconds, that is t=0 to t=1.80s

distance=_________________________________

A plane with a mass of 940kg is suddenly buffeted by a wind force directed to the right as shown. the wind force vs. time function is Fwind=5500-140e^3t. determine the sideward sliding distance if the plane is buffeted for 1.80 seconds, that is t=0 to t=1.80s distance=_________________________________

Explanation / Answer

F = 5500-140e^3t

a = F/m = (5500-140e^3t)/940 = 5.851 - 0.14894 e^(3t)

v = int{a} = int{5.851 - 0.14894 e^(3t)} = 5.851 * t - 0.14894 (1/3) e^(3t) = 5.851 * t - 0.049647 e^(3t)

x = int{v} = int{ 5.851 * t - 0.049647 e^(3t)} = 2.9255 * t^2 - 0.016549 e^(3t)

from t=0 to t=1.8s

x = (2.9255 * 1.8^2 - 0.016549 e^(3*1.8)) - (2.9255 * (0)^2 - 0.016549 e^(3*0))

x = 5.8145652 - (-0.016549)

x = 5.83 m

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