A man standing in front of a vertical cliff fires a gun. He hears the echo after 3.5 seconds. On moving closer to the cliff by 84 m, he hears the echo after 3 seconds. Calculate the distance of the cliff from the initial position of the man.

Explanation

To solve the problem step by step, we will use the information given about the echoes and the distances involved.

### Step 1: Define Variables
Let:
- \( d \) = distance from the man’s initial position to the cliff (in meters)
- \( v \) = speed of sound (in meters per second)
- \( t_1 = 3.5 \) seconds (time taken to hear the first echo)
- \( t_2 = 3 \) seconds (time taken to hear the second echo)
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