Finding height of flower pot dropper above you

[mfiorillo919]

Homework Statement

As you look out of your dorm window, a flower pot suddenly falls past. The pot is visible for a time t, and the vertical length of your window is Lw. Take down to be the positive direction, so that downward velocities are positive and the acceleration due to gravity is the positive quantity g. From what height h above the bottom of your window was the flower pot dropped?Express your answer in terms of Lw, g, t.
Assume that the flower pot was dropped by someone on the floor above you (rather than thrown downward).

Homework Equations

Not sure where to even begin

The Attempt at a Solution

Well I know that i need to use the kinematic equation that relates initial and final velocities, acceleration, and distance traveled, so that I can solve for h, but all the equations are including time in them and I'm not sure what I'm missing. Any help would be appreciated!

 

[Nugatory]

You know how long it took the dropped object to move from the top of the window to the bottom of the window, and you know the height of the window. That's enough information to calculate the speed of the object as it passed the top of the window.

 

[mfiorillo919]

how would i figure out the time, i know the initial time is 0, and the initial velocity is 0 and acceleration is gravity, how would i put these terms in the into an equation though to find out the height

 

[NascentOxygen]

While the pot is outside your window, it is free-falling under gravity. As it comes into view at the top of the window pane, the pot has a velocity which you could denote as u. You don't know much about u, but you do know that, with that initial velocity, and falling under gravity, the pot travels a distance Lw in t seconds. Do you have an equation that relates all those parameters? That will get you started.

 

[asteriatic]

First, we need to define our variables. Let h be the height of the flower pot above the bottom of the window, Lw be the vertical length of the window, g be the acceleration due to gravity, and t be the time the flower pot is visible.

Next, we can use the kinematic equation for displacement to relate these variables:

h = Lw + 0.5gt^2

Since we are assuming the flower pot was dropped, its initial velocity is 0, so we can simplify the equation to:

h = 0.5gt^2

Now, we need to find a way to express t in terms of Lw and g. We can use the kinematic equation for velocity to do this:

v = gt

Since the flower pot is falling at a constant velocity, we can set its final velocity to 0, and solve for t:

0 = gt

t = 0

Now we can substitute this value for t into our original equation for h:

h = 0.5g(0)^2

h = 0

This means that the height of the flower pot above the bottom of the window was 0, which makes sense since it was dropped from the floor above. So the answer to the question is simply:

The flower pot was dropped from a height of 0 above the bottom of the window.