A helicopter is flying in a straight line over a level field at a constant speed

Question

A helicopter is flying in a straight line over a level field at a constant speed of 6.2 m/s and at a constant altitude of 11.5 m. A package is ejected horizontally from the helicopter with an initial velocity of 10.0 m/s relative to the helicopter, and in a direction opposite the helicopter's motion.

a) Find the initial velocity of the package relative to the ground.

b) What is the horizontal distance between the helicopter and the package at the instant the package strikes the ground?

c) What angle does the velocity vector of the package make with the ground at the instant before impact, as seen from the ground?

Explanation / Answer

a)

initial velcoity relative to the ground = 10-6.2 = 3.8 m/s

b)

initial vertical velocity = 0

S = .5at^2

t = 1.532 s

so package travels a distance = 3.8*1.532 = 5.82 m

helicopter travels a distance = 6.2*1.532 = 9.5 m

distance between tehm = 9.5 + 5.82 = 15.32 m

c)

vertical velcotiy = at = 9.8* 1.532= 15.0136

horizontal velcoity remains same = 3.8 m/s

angle = tan-1(15.0136/3.8) = 78.8 degrees

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