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 of motion for vertical motion:
h = Lw + (1/2)gt^2
Here's how to obtain this equation:
1. Start with the general equation for the vertical position (y) as a function of time (t) for an object in free fall:
y = y0 + v0t + (1/2)gt^2
where y0 is the initial position, v0 is the initial velocity, and g is the acceleration due to gravity.
2. In this case, the flower pot was dropped (so v0 = 0) from a height h above the bottom of your window. Therefore, y0 = h.
3. Since we are interested in the height above the bottom of your window (h), we can substitute y for Lw (the vertical length of your window).
4. Rearrange the equation to obtain the height h:
h = Lw + (1/2)gt^2
So, the height h above the bottom of your window from which the flower pot was dropped can be expressed as Lw + (1/2)gt^2, where Lw represents the vertical length of your window, t represents the time the flower pot is visible, and g represents the acceleration due to gravity.