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.

Hint 1for Part A. How to approach the problem
The initial velocity of the pot is zero. Find the velocity vb
of the pot at the bottom of the window. Then using the kinematic equation that relates initial and final velocities, acceleration, and distance traveled, you can solve for the distance h
.
Hint 2for Part A. Find the velocity at the bottom of the window
What is the velocity vb
of the flower pot at the instant it passes the bottom of your window?
Express your answer in terms of Lw
, t
, and g
.

Hint 3for Part A. The needed kinematic equation
To solve this problem most easily, you should use the kinematic equation v2f−v2i=2a(xf−xi)
. Note that you are looking for xf−xi
, the distance traveled by the flower pot from the moment it was dropped until it reaches the height of the bottom of your window.