The problem involves calculating the depth of a canyon based on the time it takes for a stone to fall and the sound of it hitting the bottom to travel back to the top. The subject area includes kinematics and the physics of sound. The original poster seeks to determine the percentage error in depth calculation when ignoring the time for sound to travel.
Some participants have provided calculations and suggested methods for determining the time components involved. There is an ongoing exploration of the implications of ignoring sound travel time on the depth calculation, with some questioning the accuracy of their percentage error results.
Participants are working under the constraints of a homework problem, which may impose specific methods or assumptions regarding the calculations. There is a noted confusion regarding the correct interpretation of the percentage error calculation.
The time needed here is the time that the stone was falling. Why did you divide by 2?munther said:the distance = 1/2 a t^2
= .5 x 9.8 x (13.4/2)^2 = 219.961 m^2
To incorporate the time delay due to the speed of sound, you'll need to set up equations and solve for the times. Hint: Set up two equations (one for the falling rock; one for the sound) relating distance and time.munther said:then how i will divide the time between the falling and the echo
Looks good to me.munther said:ok
d= .5xgxt1 = 343t2
t1+t2 =13.4
by solving both equations
t1= 11.51
t2= 1.89
then the depth = 648.9 m
is it right
Right. (You have a typo in your formula--that should be t^2.)is the second depth when time = 13.4 for the d=.5x9.8xt
You need to read the question very carefully. I think they are asking for the percentage error the incorrect method (that ignores the sound travel time) introduces with respect to the correct method. The correct measurement should be in the denominator.munther said:thanks
i posted it ...but it is wrong!
(879.844-648.9)/(879.844)=26.2% xxx Wrong xxx !
why??