Question

Trying to determine its depth, a rock climber drops a pebble into a chasm and hears the pebble strike the ground 3.36 s later.

(a) If the speed of sound in air is 343 m/s at the rock climber's location, what is the depth of the chasm? m

(b) What is the percentage of error that would result from assuming the speed of sound is infinite? %

Answer 1

here,

a)

let the depth of chasm be h

the speed of sound , v = 343 m/s

the total time taken , t = time taken by rock to hit the ground + time taken by sound

t = (2 h /g) + (h /v)

3.36 = ( 2 * h /9.81) + (h / 343)

solving for h

h = 50.62 m

the depth of chasm is 50.62 m

b)

when the speed of sound is infinite

the depth of chasm , h' = 0.5 * g * t^2

h' = 0.5 * 9.81 * 3.36^2 m

h' = 55.37 m

the % of error , % = (h' - h)/h * 100

% = (55.37 - 50.62) /50.62 * 100

% = 9.39 %