A man loses 20% of his velocity after running through 108 m. Find maximum distance he can run

To solve this problem, we need to use the formula for the distance covered under uniform retardation, which is given by:

v² = u² - 2as

where: v is the final velocity, u is the initial velocity, a is the acceleration (which is negative since it's retardation), and s is the distance covered.

From the problem, we know that the man loses 20% of his velocity after running 108 m. This means that his final velocity (v) is 80% of his initial velocity (u). We can express this as:

v = 0.8u

Substituting this into the distance formula gives us:

(0.8u)² = u² - 2as

Solving for a gives us:

a = (u² - (0.8u)²) / (2s)

Substituting the given distance s = 108 m into this equation gives us the retardation a.

Now, the maximum distance the man can run is when his velocity becomes zero. We can find this by substituting v = 0 into the distance formula:

0 = u² - 2as

Solving for s gives us:

s = u² / (2a)

This will give us the maximum distance the man can run.