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 200 mph at an altitude of 950 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 = 9.80 m/s^2 .

Part 1. 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 200 mph in the horizontal direction.

Part 2. 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 3. What is the speed of the package when it hits the ground?

Explanation / Answer

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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 240 mph at an altitude of 750 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/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 240 mph in the horizontal direction.

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?

ince the altitude of the plane H is given and ones dropped the package will be in free fall (excluding air resistance) falling with down with acceleration g for a time t
H=0.5gt^2

The time it takes for the package to fall is

t=sqrt(2H/g)
t=sqrt(2 x 750/9.81)=12.4s

b) then if the plane flies with horizontal speed of V we have
D=Vt
since 1 mph= 0.4472 m/s
240 mph= 107.3 m/s
D= 107.3 x 12.4 =1330 m

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