Trying to determine its depth, a rock climber drops a pebble into a chasm and he

Question

Trying to determine its depth, a rock climber drops a pebble into a chasm and hears the pebble strike the ground ,. later. (a) If the speed of sound in air is a 343 m s the rock climber's location, what is the depth of the chasm? 60 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m (b) What is the percentage of error that would result from assuming the speed of sound is infinite? Need Help? ReadtMaster t

Explanation / Answer

Time taken to reach the bottom of chasm is 't'.

Time taken for sound to come back up a distance is [(3.62 s) - t].

Using equation of motion 2, we have

y = y0 + v0 t + (1/2) a t2

(0 m) = h + (0 m/s) t - (0.5) (9.8 m/s2) t2

h = (4.9 m/s2) t2                                                              { eq.1 }

We know that, d = vair t'

h = (343 m/s) [(3.62 s) - t]

h = (1241.6 m) - (343 m/s) t                                             { eq.2 }

Inserting the value of 'h' in eq.2 & we get -

(4.9 m/s2) t2 = (1241.6 m) - (343 m/s) t

(4.9 m/s2) t2 + (343 m/s) t - (1241.6 m) = 0

it's an quadratic equation.

t = - 73.4 sec      OR    t = 3.45 sec

Therefore, the depth of chasm which will be given by -

h = (4.9 m/s2) t2   

h = [(4.9 m/s2) (3.45 s)2]

h = 58.3 m

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