Skydiver

Definition

A skydiver is an individual who jumps from an aircraft and falls freely before deploying a parachute to slow their descent. The motion and forces experienced by a skydiver can be analyzed using calculus, particularly through integration.

5 Must Know Facts For Your Next Test

1. The velocity of a skydiver can be represented as the integral of acceleration over time.
2. The position function of a skydiver can be obtained by integrating the velocity function.
3. Air resistance plays a significant role in the calculus-based analysis of a skydiver's motion, often modeled with differential equations.
4. The Fundamental Theorem of Calculus connects the derivative of the position function to the velocity function for a skydiver.
5. Terminal velocity occurs when the force due to gravity is balanced by air resistance, resulting in zero acceleration.

Review Questions

• How do you use integration to find a skydiver's position function given their velocity?
• What role does air resistance play in determining the terminal velocity of a skydiver?
• Explain how the Fundamental Theorem of Calculus applies to the motion analysis of a skydiver.

Related terms

Velocity: The rate at which an object's position changes with respect to time; for a skydiver, it is found by integrating acceleration.

Acceleration: The rate at which an object's velocity changes with respect to time; for a skydiver, it includes gravitational pull minus air resistance.

Terminal Velocity: The constant speed that a freely falling object eventually reaches when the resistance prevents further acceleration.