A man fired a bullet against a wall and hears an echo after 2s. he walks 80 m towards the wall and fired bullet, such that he hears echo after 1s. If the distance from wall to the second fired place is 80 × y, then find y

The problem is about the speed of sound and how it travels.

First, let's understand the concept of echo. When the man fires the bullet, the sound travels to the wall and bounces back to him. This is the echo he hears. The time it takes for the sound to travel to the wall and back is 2 seconds in the first scenario.

The speed of sound in air is approximately 340 m/s. So, in 2 seconds, the sound travels 2*340 = 680 meters. However, this is the round trip distance (to the wall and back). So, the distance from the man to the wall in the first scenario is 680/2 = 340 meters.

In the second scenario, the man walks 80 meters towards the wall and fires the bullet again. This time, he hears the echo after 1 second. So, the sound travels 1*340 = 340 meters (round trip). Therefore, the distance from the man to the wall in the second scenario is 340/2 = 170 meters.

Since the man walked 80 meters towards the wall, the original distance (340 meters) minus the distance he walked (80 meters) should equal the distance in the second scenario (170 meters).

So, 340 - 80 = 260 meters.

But the problem states that the distance from the wall to the second fired place is 80y. So, we can set up the equation 80y = 260. Solving for y gives us y = 260/80 = 3.25.

So, y = 3.25.