A free fall problem (Physics)?

Question

Consider a five floored building, the windows of which are seperated by equal vertical distances. Imagine bricks are thrown from each window at the same time

Which brick will hit the floor first and explain the pattern of the time taken for each brick to hit the ground (i.e., if they hit the ground at increasing or decreasing time intervals)?

Answer 1

the brick thrown from the lowest window will hit first followed by each brick thrown from the window immediately above the brick that just hit. the interval between hits decreases because velocity is proportional to the square of the time it is in the air. As it falls further it is speeding up, thus it takes less time to cover the distance between two windows the further it falls.

Answer 2

I assume the question should read "Which brick will hit the **ground** first...". If this is right, then the brick thrown from the bottom floor will hit first, since it has the least distance to fall.



A nice trick to answer the other part of the question is to visualize an observer watching all five bricks as they are thrown out the windows. They start out evenly spaced, and are all affected by gravity the same way, so as they accelerate downward, they stay exactly the same distance apart until they reach the ground! This means you could do the same experiment out of a ten story building using just the top 5 floors, and you would get the same basic answer (although the actual times would be different).



Given that the *distance* between each successive brick (1st fl, 2nd fl, 3rd... etc) is the same, what about the *time*? Well, each successive brick has been accelerating a longer time, so is going faster by the time it reaches the ground, so the bricks hit the ground at decreasing intervals.

Answer 3

Instead of visualising, give the building dimensions. Say, 4m. per floor.

The 1st. brick falls 4m. The second, 8m. The third, 12m. the fourth, 16m. The last falls 20m.

Time = sqrt. (2h/g) secs.

1st brick takes 0.9 secs.

2nd. brick takes 1.278 secs.

3rd. brick takes 1.565 secs.

4th. brick takes 1.8 secs.

5th. brick takes 2.02 secs.

Then, study the time gaps.

between 1 and 2 = (1.278 - .9) = 0.378 secs.

Between 2 and 3 = (1.565 - 1.278) = 0.287 secs.

Between 3 and 4 = (1.8 - 1.565) = 0.235 secs.

between 4 and 5 = (2.02 - 1.8) = 0.22 secs.

Then you can see how the time intervals are shortening, the higher the bricks start from. They are decreasing.

Answer 4

if height of first floor is H m then time before the brick from first floor reaches the ground

t=(2*H/9.81)^0.5 s

times before the bricks from second......... floors reach the ground are

2^0.5*t, 3^0.5*t.....s