To solve this problem, we need to determine the time, denoted as
t0, at which the separation between two falling stones becomes H . The second stone starts falling
∆t seconds after the first stone.
Distance Fallen by the First Stone (
S1 ):
The first stone falls for
t0 seconds, so the distance it covers is given by:
S1=‌gt02Distance Fallen by the Second Stone
(S2) :
The second stone starts falling
∆t seconds after the first, so it falls for
(t0−∆t) seconds. Thus, the distance it covers is:
S2=‌g(t0−∆t)2 Distance of Separation (H):
The separation distance between the two stones is:
H=S1−S2=‌gt02−‌g(t0−∆t)2Simplifying the equation:
H‌=‌gt02−‌g(t02−2t0∆t+(∆t)2)‌=‌g⋅(2t0∆t−(∆t)2)‌=g⋅(t0∆t−‌∆t2) Expression for
t0 :
Solving the above equation for
t0, we have:
‌H=g(t0∆t−‌∆t2)‌t0∆t=‌+‌∆t2‌t0=‌+‌ Therefore, the time
t0 at which the separation between the two stones becomes H is given by:
t0=‌+‌