A 60-kg and a 90-kg skydiver jump from an airplane at an...

Name: Problem 21, Chapter 5: College Physics
Uploaded: 2020-06-28T03:26:05-08:00
Duration: 2 min 57 s
Channel: Mayukh Banik
Description: A 60-kg and a 90-kg skydiver jump from an airplane at an altitude of 6000 m, both falling in a headfirst position. Make some assumption on their frontal areas and calculate their terminal velocities. How long will it take for each skydiver to reach the ground (assuming the time to reach terminal velocity is small)? Assume all values are accurate to three significant digits.

A 60-kg and a 90-kg skydiver jump from an airplane at an altitude of 6000 m, both falling in a headfirst position. Make some assumption on their frontal areas and calculate their terminal velocities. How long will it take for each skydiver to reach the ground (assuming the time to reach terminal velocity is small)? Assume all values are accurate to three significant digits.

Key Concepts

Drag Force

Drag force is the resistive force exerted by a fluid (such as air) on an object in motion. It depends on factors like the fluid density, the object's speed (typically proportional to the square of the speed), the frontal area, and the drag coefficient, which encapsulates the effect of the object's shape on the resistance offered by the fluid.

Force Equilibrium at Terminal Velocity

At terminal velocity, the gravitational force (mg) is balanced by the drag force. This balance allows for the derivation of an expression for terminal velocity by equating mg with the drag equation, usually written as ½ * C_d * ? * A * v², where each parameter contributes to how quickly an object falls under air resistance.

Terminal Velocity

Terminal velocity is the constant speed reached by a falling object when the net force acting on it becomes zero. This occurs when the upward drag force exactly balances the downward gravitational force, making the acceleration zero, and resulting in a steady fall speed.

Assumptions in Modeling Free-Fall with Air Resistance

Modeling the fall of objects like skydivers often involves simplifying assumptions such as a constant drag coefficient, uniform air density, and an almost instantaneous achievement of terminal velocity. These assumptions allow us to treat the motion as if the object is falling at a constant speed (its terminal velocity) for most of its descent, simplifying the calculation of the time to hit the ground.

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