Chapter 04, Problem 133 A helicopter is flying in a straight line over a level f

Question

Chapter 04, Problem 133 A helicopter is flying in a straight line over a level field at a constant speed of 6.00 m/s and at a constant altitude of 9.60 m. A package is ejected horizontally from the helicopter with an initial velocity of 13.0 m/s relative to the helicopter and in a direction opposite the helicopter's motion. (a) Find the initial speed 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? (a) Number (b) Number (c) Number Units Units Units

Explanation / Answer

Given,

v = 6 m/s ; h = 9.6 m ; vi = 13 m/s ;

a)the packages velocity with respect to ground will be:

v = 13 - 6 = 7 m/s

Hence, v = 7 m/s (or -7 m/s)

b)t = sqrt (2y/g)

t = sqrt (2 x 9.6/9.81) = 1.39 s

t = 1.39 s

X = v t

X = 13 x 1.39 = 18.1 m

Hence, X = 18.1 m

c)v' = 9.81 x 1.39 = 13.64 m/s

theta = tan^-1 (13.64/7) = 62.83 deg

Hence, theta = 62.83 deg

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