An alpinist with a mass of m=\SI75kg is fastened to an elastic rope with a length of L=\SI6m. The other side of the rope is attached to a cliff. After climbing to a height of 6 meters from the attachment point the alpinist falls. Find the rope’s maximal elasticity coefficient k, knowing that a maximal pulling force of the rope that a human can tolerate is T=25mg. Do not account for air resistance.