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

Question

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 220 at an altitude of 750 . 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 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 = 9.80 . Part A After a package is ejected from the plane, how long will it take for it to reach sea level from the time it is ejected? Assume that the package, like the plane, has an initial velocity of 220 in the horizontal direction. Part B If the package is to land right on the island, at what horizontal distance from the plane to the island should the package be released? Part C What is the speed of the package when it hits the ground?

Explanation / Answer

Part A)

The package will have zero initial velocity in the y direction, therefore we can use that information to determine how long it will take to reach the ground

d = vot + .5at2

900 = (0) + (.5)(9.8)(t2)

t = 13.55 sec

Part B)

For this part, we first must convert 230 mph to m/s

1 mph = .447 m/s, thus 230 mph = 102.81 m/s

d = vt

d = (102.81)(13.55)

d = 1393 m

Part C)

The final velocity in the y direction is found from

vf = vo + at

vf = (0) + (9.8)(13.55)

vf = 132.8 m/s

The resultant velocity is found by the pythagorean theorem (the x velocity does not change)

v = [(132.8)2 + (102.81)2

v = 167.9 m/s

In case you need that converted back to miles per hour, that is 376 mph

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