Math Problem Statement

Trying to determine its depth, a rock climber drops a pebble into a chasm and hears the pebble strike the ground 4.00 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?

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

Solution

Let's solve this again step-by-step.

(a) Determining the depth of the chasm:

We need to account for two separate phases:

  1. Time for the pebble to fall:
    • The pebble falls for a certain time t1t_1, during which it accelerates due to gravity.
  2. **Time for the sound to travel

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Kinematics
Speed of Sound
Time
Distance

Formulas

d = (1/2)gt^2
d = v_sound * t_sound
t_total = t_fall + t_sound

Theorems

Kinematic equations for free fall
Speed of sound in air

Suitable Grade Level

Grades 10-12

Related Recommendation

Determining Chasm Depth Using Kinematics and Sound Propagation

Calculating the Depth of a Chasm with Free Fall and Sound Propagation

Physics Problem: Calculating the Depth of a Well Using Free Fall and Speed of Sound

Calculate the Height of a Cliff Using Free Fall and Sound Propagation

Calculate the Depth of a Well Using Time and Speed of Sound