   Chapter 14, Problem 8P

Chapter
Section
Textbook Problem

A stone is dropped from rest into a well. The sound of the splash is heard exactly 2.00 s later. Find the depth of the well if the air temperature is 10.0°C.

To determine
The depth of the well

Explanation

Given Info: Temperature of the air is 10°C .

Formula for speed of sound in air is,

v=331m/s1+TC273

• TC is the temperature of air in Celsius.

Substitute 10°C for TC in the above expression to get v .

v=331m/s1+10°C273=337m/s

Formula to calculate the depth of the well,

h=gt22 (1)

• h is the depth of the well
• g is the acceleration due to gravity
• t is the time for the stone to fall in to the well.

Formula for the time for the sound to travel back up the well is,

t'=hv

• t is the time taken for the sound to travel back up the well.

The time taken for the sound to travel back up the well is difference between,

t=2.00st1

Use 2.00st1 for t in t'=h/v to rewrite,

2st=hv (2)

Use gt2/2 for h in the above equation to rewrite it in the form of quadratic equation

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