Acceleration and distance :S ?

[simply_me_xo]

ok so here's the question

She picks up a large stone and drops it into a pit, listening for the sound of it hitting the bottom. The pit has a uniform temperature of 8 degrees celsius. From the time the rock leaves her hadn to the time the sound of it striking bottom reachers her ears, 24 seconds pass. What is the depth of this whole?



... okay so i know that acceleration is change in velocity over time.
this gives you the time , and also the temperature which by using v=332+0.6(T) will give me a velocity

i'm assuming that the initial velocity would be 0 ? ... and then using the formula above the other velocity would be 336.8 m/s

thennnnnn do 336.8 divided by time ( 24 s ) so get acceleration ... but then how do i get the distanceee?

d=t*v butttt wouldn't acceleration effect that somehow?

 

[tabchouri]

you have two phases in the system:

phase 1. the stone is falling in free fall state (if we neglect the air friction), takes it some time

-transition- the stone hits the bottom, this transition does not take time (assume it is instantaneous)

phase 2. the sound propagates from the bottom to the ears of the girl

now the total time (24s) is the sum of durations of phase 1 & phase 2

- I hope this helps you

BTW, i don't see what does the temperature do here, unless you considering the velocity propagation of sound in air as funtion of temperature (which i doubt in such situation)

 

[simply_me_xo]

thanksss , i don't seee how that gets me the depth of the whole though ?

 

[learningphysics]

Write an equation for the depth.

 

[simply_me_xo]

like just d=v*t
doesnt the acceleration effect that somehow though?

 

[tabchouri]

ok, let's see more in details

phase 2- speed of sound in air Vs = 1200 m/s = d / t2 , so t2 = Vs / d, also d = Vs t2

phase 1- gravity is the only force applied,
F=m a = m G, so G = a = dv/dt =d²y/dt², so v(t) = G t + V(0), so y(t) = G t² / 2 + v(0)t + y(0)
if you consider v(0) = 0 & y(0)=0, then y(t) = G t² / 2
then at the time of the impact (which is t1), y(t1) = d

so G t1² / 2 = d
or d = Vs t2

and also t1 + t2 = 24 seconds

the rest is clear