(Figure 1) A relief airplane is delivering a food package to a group of people s

Question

(Figure 1) 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 472 km/hour at an altitude of 975 m . 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 = 9.80 m/s2

Explanation / Answer

V=472km/hr=131.1m/sec

H=975m

g=9.8 m/s^2

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 472km/hr in the horizontal direction.

Answer:

S=ut+1/2at^2

U=0

975=1/2*9.8*t^2

t=14.1 sec—answer

b) If the package is to land right on the island, at what horizontal distance D from the plane to the island should the package be released?

Answer:

S=ut+1/2at^2

S=131.1*14.1+1/2*0*t^2

Here a=0 since there is no horizontal acceleration

S=1848.5m—answer

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