Physics Question/Problem... Can you do it? :D?

[jakeydav]

40. Frederick comes up with the following scheme to measure a buildings height. A timing mechanism is set up which measures the time taken by an object dropped from the top of the building to fall the last 2.0 m before it hits the ground. The object is found to take 0.125 s to move this last 2.0m. How high is the building?

Show how you did it and explain it also.
(acceleration of gravity is -9.8m/s-squared)

[hari b]

well,
according to the data, the object has fallen 2.0 m in 0.125 s with the acceleration of 9.8 m/s^2. so, by using the equation of motion s = ut + 1/2 at^2, by applying the values
2.0 = (u x 0.125) + ( 1/2 x 9.8 x 0.125^2),
you will get 'u' as 15.4 m/s. this speed is the initial speed of the object when it is at 2.0 m above the ground, which is the final speed of the object from the top of the building, above 2.0 m ground. again by applying the equation of motion,
v^2 - u^2 = 2gh,
where 'v' is the final speed at 2.0 m above the ground, and 'u' is the initial spped of dropping which is zero.
by substituting the values into the equation above, you will get 'h' value as 12.0 m, this is the height above 2.0 m, and so the total height of the building is 12.0 + 2.0 = 14.0 m

[Deep Sky Blue]

Let s be measured downwards. Then you know that

v = gt and s = v0 * t + 1/2 g * t^2 where v0 = 0.

Then

H - 2.0 = 1/2 g * t^2 and H = 1/2 g * (t + 0.125)^2

or

1/2 g*[ (t + 0.125)^2 - t^2 ] = 2.0
0.250 * t + 0.0156 = 4.0 / 9.8 = 0.408

t = 0.393 / 0.250 = 1.570 sec

so that

H = 1/2 * 9.8 * (1.570 + 0.125)^2 = 14.08 m

Hope this helps.