Problem 1: 20 Points A helicopter drops a supply package to stranded people on a

Question

Problem 1: 20 Points A helicopter drops a supply package to stranded people on an island. At the instant the package is dropped, the helicopter is 80 m above a clearing area and lying at 36 m/s at an angle of 37 above horizontal. Choose the origin to be on the ground and directly below the helicopter when the package is dropped. a) Draw S vs t, sy vs t, vs vs t, and vy vs t graphs of the package's motion b) How long is the package in the air? c) Where does the package land? d) If the helicopter continues to fty at constant velocity, what are the coordinates of the helicopter when the package lands?

Explanation / Answer

Given,

v = 36 m/s ; H = 80 ; theta = 37 deg

a)Graphs uploaded

b)the vertical and horizontal velocities are :

vy = 36 sin37 = 21.67 m/s

vx = 36 cos37 = 28.75 m/s

We know from eqn of motion

S = ut + 1/2 at^2

-80 = 21.67 t - 0.5 x 9.8 x t^2

4.9t^2 - 21.67 t - 80 = 0

This gives us,

t = 6.82 s and -2.39 s

Hence, t = 6.82 s

c)The package land at

D = vx t

D = 28.75 x 6.82 = 196.08 m

Hence, D = 196.08 m

d)The helicopter would be at

X = vx t = 196.08 m

Y = 80 + 21.67 x 6.82 - 0.5 x 9.8 x 6.82^2 = -0.121 m

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