91Ó°ÊÓ

When an object falling through the air reaches a constant speed, we say it has hit its terminal velocity. This is a critical point where the downwards pull of gravity is perfectly balanced by the upwards drag force. In other words, the net force is zero, and there's no acceleration occurring, as per Newton's second law. The skysurfer mentioned in our exercise has achieved this balance at a speed of 60 m/s. At terminal velocity, the speed does not increase despite the continual gravitational pull because the air resistance, or drag force, increases with speed and eventually matches the gravitational force acting on the object.

Understanding terminal velocity is essential for accurately assessing situations like the skysurfer's fall, and it can also apply to other contexts, such as automotive design, where engineers work to minimize drag to increase a car’s efficiency.

Gravitational force is the attraction between two masses, such as between our planet and the skysurfer. It's this force that causes objects to fall towards Earth when they are dropped. The formula to calculate this force when dealing with objects near the Earth's surface is given by the product of the object’s mass (m) and the acceleration due to gravity (g), which is approximately 9.81 m/s². For our skysurfer, with a mass of 75 kg, the gravitational force can be calculated using the formula
\[ F_g = m \cdot g \].
Substituting in the values gives us a force of
\[ F_g = 75.0 \, \mathrm{kg} \cdot 9.81 \, \mathrm{m/s^2} = 735.75 \, \mathrm{N} \],
indicating that our Earth is pulling the skysurfer down with a force of 735.75 N. This force is also equal to what we commonly refer to as the object's 'weight'.

Power in physics refers to the rate at which work is done or energy is transferred over time. To calculate it, we typically use the formula:
\[ \text{Power} = \text{Force} \times \text{Velocity} \],
where force is the constant force acting on an object, and velocity is the constant speed of the object. For objects falling at terminal velocity, the power calculation represents the rate of mechanical energy loss as they descend, assuming no other form of energy is involved. In the case of the skysurfer, we determined the gravitational force (which is equal to the opposing drag force at terminal velocity) and multiplied it by the constant terminal velocity. Doing the math gives us
\[ \text{Power} = 735.75 \, \mathrm{N} \times 60.0 \, \mathrm{m/s} = 44145 \, \mathrm{W} \].
The result, 44145 W, indicates a significant amount of energy conversion occurring as the skysurfer descends at a steady pace towards the Earth.