Final answer:
To find the height of a cliff from which a stone is dropped and travels 44.1m in the last second, we use the equations of motion for an object under gravity. The 1:3:5 method is not directly applied but the information leads us to solve for the total time of fall, and subsequently, we use kinematic equations to find the total height of the cliff.
Step-by-step explanation:
The question asks to find the height of a cliff given that a stone is observed to travel 44.1 meters in the last second before it hits the ground. This is a classic problem in physics involving kinematics and the equations of motion for an object in free fall under the influence of gravity.
To solve this, we can use the 1:3:5 method, which stems from the fact that the distance traveled by an object in free fall from rest varies as the square of the time. This implies that if an object falls for t seconds, and in the last second travels a distance d, then the total time of fall is ∙t∙, and the total height H from which the stone fell is given by d multiplied by the sum of the series (1+3+5+...+(2t-1)).
However, since we know the distance traveled in the last second, we do not directly apply the full series sum here. Instead, we use the formula for the distance fallen in the nth second dn = u + a(n-0.5), where u is the initial velocity (0 m/s in this case), a is the acceleration due to gravity (9.8 m/s²), and n is the last second during which the stone travels. We can rearrange this to solve for n, and then calculate the total height H using the formula H = 0.5an².
By substituting the given values and solving, we can find the total time of fall and with that the height of the cliff. It's important to note that the answer arrived by this method concisely uses principles of uniformly accelerated motion.