Find the initial velocity of the package relative to the ground. A helicopter is

Question

Find the initial velocity of the package relative to the ground. A helicopter is flying in a straight line over a level field at a constant speed of 6.4 m/s and at a constant attitude of 11.0 m. A package is ejected horizontally from the helicopter with an initial velocity of 14.0 m/s relative to the helicopter, and in a direction opposite the helicopters motion. Find the initial velocity of the package relative to the ground. What is the horizontal distance between the helicopter and the package at the instant the package strikes the ground? 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) 14-6.4 = 7.6 m/s

b)

y direction

y = y0 + v0y t + 1/2 a t^2

0 = 11 - 0.5*9.81*t^2

t=1.49 s

x dirction

v relative to helicopter = 11

x = v t = 14*1.49= 20.86 m

c) vx = 7.6 m/a

vy = -g t = -9.81*149= -14.61 m/s

angle = arctan(vy/vx) = arctan(14.61/7.6)= 62.51 degrees

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