(a)

The stiffness of the cord is related to the amount of stretch by the equation .

Where,

weight of the jumper(pounds),

cords stiffness(pounds per foot),

free length of the cord(feet),

stretch (feet).

Here , , and .

Consider .

Substitute and in .

The function .

First solve the equation .

Solve the equation by using quadratic formula.

Quadratic formula : .

Compare with standard form of quadratic equation .

.

Solution :

Since the value of stretch cannot be negative, consider .

Therefore, when the person of jumps off the ledge using rope, the rope will stretch less than .

(b)

The free length of the cord is .

When the person having jumps from the ledge using the cord, he falls freely upto .

Due to this weight the rope stretches by .

Thus, the total length at which the person falls is .

Since the safety requirement does not permit the person to be no closer than to the ground, the rest of the length from the ledge so as to reach the ground will be .

So, the minimum height required for the ledge is .

Therefore, the ledge should be at least above the ground for a  jumper. 

(a)

The stretch is less than .

(b)

The ledge should be at least above the ground for a  jumper.