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 362 km/hour at an altitude of 625 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 .

Part AAfter a package is dropped from the plane, how long will it take for it to reach sea level from the time it is dropped? Assume that the package, like the plane, has an initial velocity of 362 km/hour in the horizontal direction.

Part 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?

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

Explanation / Answer

here,

1 km/hr = 0.278 m/s

Horizonatl Velocity, Vx = 362 kh/hr = 100.556 m/s

Height of plane, h = 625 m

Part A:
Fromt hird Eqn of motion, vy = sqrt(2*g*h)
(Vy is vertical velocity of package)

Vy = sqrt(2*9.8*625)
Vy = 110.68 m/s

From First eqn of motion, Solving time takne by package to reach ground,

t = vy/g = 110.68/9.8
t = 11.294 s

Part B:
From Second Equation fo motion, x = vx*t
x = 100.556 * 11.294
x = 1135.679 m

the horizonatl distance D = x = 1135.679 from the palne to the island.

Part C:

Part C:
From Second Equation of motion,

h = v*t

solving for Velocity when it reach ground, v = h/t = 625/11.294
v = 55.34 m/s

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