in this illustration, we'll discuss the calculation of a tower height.
we are given that a stone falling, from the top of a vertical tower, has descended x meter.
when another is let to fall from a point y meter bellow the top.
if they fall from rest and reach ground together we are required to find the height of the
tower in this situation.
here if we draw the picture.
say this is a tower of height h, and a stone 1, is drop from the top. and when, it will
descend, by distance x meter.
then obviously the time taken in descending x meter we can write as root 2 x by g. and
then another stone is dropped obviously at this point it'll attain some speed.
and another stone 2 is dropped.
from a height, or a depth y meter bellow the top. and we are given that this stone 1 and
2 will reach the bottom of ground, the bottom of this tower together the ground together.
so in this situation we can say.
total time.
in which.
stone 1.
hits the ground is, this total time for, the stone 1 and hitting the ground is root 2 h
by g because it is freely falling from rest.
by height h. this height h we can write separately.
and out of this time root 2 x by g is gone when, 2 is dropped.
so we can write time.
available.
for stone 2. in reaching ground is.
this time can be return as t 2 and this root of, twice of, h minus y by g. and this time
we can, equate with root 2 h by g minus.
root of 2 x by g because out of this root 2 x by g this much time is gone. and the remaining
time is the time taken by the tone 2 in reaching ground.
and it has to fall.
in free fall from rest, a height h minus, y. now if we simplify this here g gets cancelled
out. and on simplifying this expression.
we can write it as 2 h minus root of twice of h minus y is equal to root 2 x. if we square
this relation, this will give us 2h plus 2 h minus 2 Y, minus of 4 times root of, h multiplied
by h minus y is equal to 2 x. here, this is a positive sign and this with negative sign.
and in this situation, if we further square this term here you can see. on lefthand side
we can write.
2 times root of.
h square minus h y which is equal
to. this, 2 h minus x plus. y, i have cancel the value of 2, numerical value 2. and if
we further square it you can see. this will give us 4 h square, minus 4 h y is equal to
4 h square. plus x plus y whole square. minus 4 h x, minus 4 h y. here 4 h square and 4
h y both gets cancelled out and if we continue over here. this would directly give us the
value of h which is x plus y hall square by 4 x. that is the final result of this problem.
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