(a)
The depth of the chasm.
(a)
Answer to Problem 80PQ
The depth of the chasm is
Explanation of Solution
Assume that the pebble falls a distance
Write the equation for the total time interval.
Here,
Rewrite the above equation for
Write the Newton’s equation of motion for the fall of the pebble into the chasm.
Here,
The initial speed of the pebble is zero. The pebble is under free fall during the time interval
Replace
The sound from the impact travels at constant speed during the time interval
Write the expression for distance covered during the time interval
Here,
Equate equations (II) and (III).
Put equation (I) in the above equation.
The above equation is quadratic in
Write the expression for the solution of the above equation.
Conclusion:
It is given that the total time interval is
Substitute
Substitute
Therefore, the depth of the chasm is
(b)
The percentage of error that would result from assuming the speed of sound to be infinite.
(b)
Answer to Problem 80PQ
The percentage of error that would result from assuming the speed of sound to be infinite is
Explanation of Solution
If the travel time for the sound of impact is ignored, it would mean that equation (II) has to be used to determine the depth.
Write the equation for the percentage of error.
Conclusion:
Substitute
Substitute
Therefore, the percentage of error that would result from assuming the speed of sound to be infinite is
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Chapter 2 Solutions
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