Solving for Time: Dropping Package from Helicopter

[atbruick]

Homework Statement

A helicopter is ascending vertically with a speed of 5.83 m/s. At a height of 121 m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground?

Homework Equations

Vfinal=Vinitial + at
or
Xfinal=Xinitial + Vinitial(t) + (1/2at)squared

The Attempt at a Solution

I tried putting in my answer from the first equation but it was wrong, and every time I try the second equation I get a negative answer which doesn't make sense.

 

[nick850]

negative time in physics doesn't really mean anything. all the negative means is that you put a negative -9.8 acceleration for gravity

the problem gives you this data:

d = 121m
vi = 5.83 m/s (initial velocity is 5.83 meters per second. yes it is negative since it's going down but we aren't going to worry about it)
a = 9.8m/s^2
t = ?

so you use this equation:
d= vi + 0.5at^2
121 = 5.83+.5*9.8*t^2
t = 4.8481 seconds

 

[atbruick]

My online homework say's that's not correct. I'm also confused on how you derived your equation?

 

[Arturo Andujo]

well i found out the velocity at the time of collision 1st with v^2 =vi^2 +2a(x-xi) to be 49.05 and then using the 1st equation i got the time to be 5.6 or 5.599

edit: if your homework was anything like mine then it was probably asking for that too and i found it easier to get that answer 1st

 

[rwisz]

I would like to point out that the equations you have attempted to use are for motion with constant acceleration, such as free fall. However, in this scenario, the helicopter is ascending vertically with a constant velocity, meaning there is no acceleration involved. Therefore, we cannot use these equations to solve for the time it takes for the package to reach the ground.

To solve this problem, we need to use the equation for displacement, which is given by:

X = X(initial) + V(t)

Where X(initial) is the initial height of the package (121 m), V is the velocity of the helicopter (5.83 m/s), and t is the time it takes for the package to reach the ground.

We can rearrange this equation to solve for t:

t = (X - X(initial)) / V

Substituting the given values, we get:

t = (0 - 121) / 5.83

t = -20.75 seconds

However, as time cannot be negative, we can conclude that the package will not reach the ground in this scenario. It will continue to ascend with the helicopter until it is released or until the helicopter changes its velocity.