After a recent hurricane, many areas in the interior of Puerto Rico were inacces

Question

After a recent hurricane, many areas in the interior of Puerto Rico were inaccessible by road. In order to quickly distribute rescue supplies, a helicopter is flying horizontally 45.0 m above the island at 35.0 mph (15.6 m/s) and drops 14.5 kg relief packages. The shape of the parachute is designed such that the package experiences negligible horizontal air resistance but descends with a constant acceleration of 4.5 m/s^2.

a) what shape is the trajectory of the fall?

b) how long will a package take to reach the ground?

c) how far infront of a target should a package be released?

d) If the package is designed to survive impacts at speeds of up to 30 m/s, will it remain intact as it hits the ground?

e) if the package was dropped vertically from a higher height, it would reach a terminal speed of 30 m/s. what is the drag constant, D, of the package?

Explanation / Answer

(a) Since helicopter has horizontal velocity therefore the packet will have the horizontal velocity and during its fall it has attained the vertical velocity as well , therefore the trajectory must be projectile.
(b) We know the vertical distance (S) = 45 m
a = 4.5 m/s2
initial vertical velocity = 0
we know that
S = ut + (1/2)at2
45 = 0 + 0.5*4.5t2
t = 4.472 s
in 4.472 s the packet will be grounded.
(c) The horizontal distance covered by the packet = horizontal velocity*time = 15.6*4.472 =69.765 m
(d) Let us consider the final velocity of the paket will be V
V = u + at = 0 + 4.5*4.472 = 20.124 m/s
This is the vertical velocity component = 20.124 m/s
Horizontal velocity component = 15.6 m/s
Final velocity = (20.1242 + 15.62)1/2 = 25.46 m/s
Since the final velocity is less than 30 m/s therefore the packet will remain intact.
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