As you took out of your dorm window, a flower pot suddenly falls past. The pot i

Question

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

Explanation / Answer

Let total time taken to fall to bottom of window be T, applying second equation of motion,

h = 0.5gT^2

also h - Lw = 0.5g(T-t)^2

h - Lw = 0.5g(T-t)^2

h - Lw = 0.5gT^2 + 0.5gt^2 - gTt

Lw = gTt - 0.5gt^2

gTt = Lw + 0.5gt^2

T = Lw/gt + 0.5t

so h = 0.5 gT^2

h = 0.5 g (Lw/gt + 0.5t)^2 answer

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