5. A package is dropped at time `t = 0` from a helicopter that is descending steadily at a speed `v_i`.
(a) What is the speed of the package in terms of `v_i, g`, and `t`?
(b) What vertical distance `d` is it from the helicopter in terms of `g` and `t`?
(c) What are the answers to parts (a) and (b) if the helicopter is rising steadily at the same speed?
`v_y = v_(yi) + a∆t`; `y_f = y_i + v_(yi)t + 1/2 a t^2`
(a)`color(red)(v_y = -v_i - g t)`
(b)`color(red)(d = -1/2 g t^2)`
(c)
part (a) `color(red)(v_y = v_i - g t)`
part (b) `color(red)(d = -1/2 g t^2)`
Set upward direction is positive.
Known: dropped at time `t=0` and `a_y = -g`
Given: `v_(yi) = -v_i`
(a)
`v_y = v_(yi) + a∆t`
`=> color(red)(v_y = -v_i - g t)`
(b)
distance package moved ` = y_p`
distance helicopter moved ` = y_h`
distance between helicopter and package is:
`d = y_p - y_h`
`y_p = y_i + v_(yi)t + 1/2 a t^2`
`y_h = y_i + v_(yi)t`
where `y_i = 0`
`d = -v_i t + 1/2(-g)t^2 - (-v_i t)`
`color(red)(d = -1/2 g t^2)`
(c)
if `v_(yi) = +v_i`
part (a) became `color(red)(v_y = v_i - g t)`
part (b) still `color(red)(d = -1/2 g t^2)`
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