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 L_w. 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).

To determine the time it takes for the flower pot to fall past your window, we can use the equations of motion.

The flower pot is initially at rest on the floor above you, so its initial velocity, u, is zero. The acceleration due to gravity, a, is equal to the acceleration in the downward direction, and we can take it to be positive.

Using the equation of motion:

s = ut + (1/2)at^2

where s is the vertical distance traveled by the flower pot, we can rearrange the equation to solve for time:

t = √(2s/a)

Since the flower pot falls past your window, its vertical distance traveled is equal to the height of your window, L_w.

Substituting these values into the equation, we get:

t = √(2L_w/g)

Therefore, to find the time it takes for the flower pot to fall past your window, you need to know the height of your window (L_w) and the acceleration due to gravity (g).