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"An Alaskan rescue plane traveling 44 m/s drops a package of emergency rations from a height of 160 m to a stranded party of explorers. The acceleration of gravity is 9.8 m/s². Where does the package strike the ground relative to the point directly below where it was released?"

A. 0 meters
B. 20 meters
C. 40 meters
D. 80 meters

User Konquestor
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1 Answer

4 votes

Final answer:

The package dropped from an Alaskan rescue plane will strike the ground approximately 251 meters from the point directly below where it was released, after falling for about 5.71 seconds.

Step-by-step explanation:

The question asks where a package dropped from an Alaskan rescue plane strikes the ground relative to the point directly below where it was released. Since the package is dropped from a moving plane, its initial velocity is horizontal at 44 m/s. The acceleration due to gravity (9.8 m/s²) will act vertically downwards. To solve this problem, we need to calculate the time it takes for the package to fall to the ground and then use this time to determine the horizontal distance it travels while falling.

First, we calculate the time (t) it takes to fall from a height (h) of 160 m using the formula h = 1/2gt², where g is the acceleration due to gravity:

160 m = 1/2 * 9.8 m/s² * t²

t² = (2 * 160 m) / 9.8 m/s²

t² = 32.65 s²

t = √32.65 s²

t ≈ 5.71 s

Now, using the horizontal speed (v) of 44 m/s, we determine how far the package travels horizontally (d) during this time: d = v * t

d = 44 m/s * 5.71 s

d ≈ 251.24 m

Therefore, the package will strike the ground approximately 251 meters from the point directly below where it was released.

Note: Since this distance is not listed in the multiple choice options given in the question, it suggests there may have been an error in the provided choices, as none of them match the correct calculated distance.

User Rob MacEachern
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7.6k points