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A package is dropped at time t = 0 from a helicopter that is descending steadily

ID: 2047230 • Letter: A

Question

A package is dropped at time t = 0 from a helicopter that is descending steadily at a speed vi.

(a) What is the speed of the package in terms of vi, g, and t?
|vp| = gt + vi m/s

(b) What vertical distance d is it from the helicopter in terms of g and t ?
d = 1/2gt2

(c) What are the answers in parts (a) and (b) if the helicopter is rising steadily at the same speed? (Use any variable or symbol stated above as necessary.)


The answers for part a are correct, I just need help with part b.

I have tried the following answers which are all incorrect:

|vp| =vi - gt, gt - vi, gt + vi

d = 1/2gt2 + 2vit, 1/2gt2 - vit

|vp| =
d =


Explanation / Answer

Set your starting reference point as at the height where the package was dropped and direction as downward


In these equations,
d = (1/2)*a*t^2 + v_i*t + d_i
v = a*t + v_i
a is equal to +g (+9.81 gravity because same direction as your reference direction)
v_i will be positive if descending (same as your reference direction) and negative if ascending (opposite to your reference direction).
d_i will be 0 (at your starting reference point)

(a) descending
| vp | = g*t + v_i (v_i uses positive sign)

(b)
d = (1/2)*g*t^2 + v_i*t

(c) ascending
| vp | = g*t - v_i (v_i uses negative sign)

d = (1/2)*g*t^2 - v_i*t

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