Summary
Highlights
Terminal velocity is reached when an object falling through a fluid (like air) experiences an air resistance force equal to its weight force. Initially, only gravity acts on the object, increasing its vertical speed. As speed increases, so does air resistance. Once air resistance equals weight, the net force becomes zero, leading to zero acceleration and a constant, maximum velocity called terminal velocity.
The calculation of terminal velocity depends on the speed of the object. At low speeds, air resistance is directly proportional to velocity (F = Kv). At high speeds, air resistance is proportional to the square of velocity (F = Dv²). For high-speed freefall, the terminal velocity is calculated as the square root of (mg/D), where 'm' is mass, 'g' is gravity, and 'D' is a proportionality constant.
The proportionality constant 'D' at high speeds depends on the density of the fluid (e.g., air), the object's projected area, and the drag coefficient. An increase in the projected area (like with a parachute) increases 'D', which in turn decreases the terminal velocity. Increasing the mass of the object, while keeping other factors constant, will increase the terminal velocity.
A 75 kg skydiver reaches a terminal speed of 55 m/s. The video demonstrates how to calculate the acceleration of the skydiver when his speed is 40 m/s and the force of air resistance when his speed is 35 m/s. These calculations involve first determining the proportionality constant 'D' using the terminal velocity, and then applying Newton's second law.
The problem concludes by asking what the new terminal speed would be if the skydiver wore a 15 kg backpack. Since the backpack primarily increases mass and does not significantly change the projected area, the proportionality constant 'D' remains largely the same. The new terminal velocity is calculated using the increased total mass (90 kg), resulting in a higher terminal speed of 60.25 m/s.