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.

Assume that the flower pot was dropped by someone on the floor above you (rather than thrown downward).

From what height h above the bottom of your window was the flower pot dropped?
Express your answer in terms of Lw, t, and g.

To determine the height h above the bottom of your window from which the flower pot was dropped, we can use the kinematic equation:

h = 0.5 * g * t^2

In this equation, h represents the height, g is the acceleration due to gravity, and t is the time the pot is visible for.

Since we are given that the vertical length of your window is Lw, we can express the height h in terms of Lw. The bottom of the window would be at a distance of 0 from the ground, so we can subtract h from Lw to find the height above the bottom of the window:

height above the bottom of the window = Lw - h

Substituting the expression for h from the kinematic equation:

height above the bottom of the window = Lw - (0.5 * g * t^2)

Therefore, the height h above the bottom of your window from which the flower pot was dropped can be expressed as Lw - (0.5 * g * t^2).