A relief airplane is delivering a food package to a group of people stranded on

Question

A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 210mph at an altitude of 750m . The positive x and y directions are defined in the figure. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g = 9.80m/s2 .

What is the speed vf of the package when it hits the ground?

Explanation / Answer

From h = 800 m, the time to impact is T = sqrt(2h/g) = sqrt(2*800/9.8) = 12.78 sec. ANS.

In that time, the package will travel X = Ux T = (200/3600)*12.78 = 0.71 miles; so the release point has to be .71 mi ~ 1142.63 m shy of X marks the spot on the island. ANS.

V = sqrt(Vy^2 + Ux^2); where Vy^2 = 2gh, so V = sqrt(2*9.8*800 + 89.4^2) = 153.86 mps = 344.18 mph at an angle theta = ATAN(-sqrt(2*9.8*800)/89.4) = -54.47 degree below the horizontal. ANS. Note Ux = 200 mph = 89.4 mps.

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