Skydiver

Definition

A skydiver is an individual who jumps from an aircraft and free-falls before deploying a parachute. The motion of a skydiver can be modeled and analyzed using calculus, particularly integration.

5 Must Know Facts For Your Next Test

1. The velocity function $v(t)$ of a skydiver can be found by integrating the acceleration function $a(t)$.
2. The position function $s(t)$ of a skydiver can be determined by integrating the velocity function $v(t)$.
3. The Fundamental Theorem of Calculus links differentiation and integration, allowing calculation of displacement from velocity.
4. Air resistance affects the acceleration of the skydiver, making it necessary to consider variable forces when setting up integrals.
5. If given initial conditions such as initial velocity or position, these constants must be considered when solving integrals for motion.

Review Questions

• How do you use integration to find the velocity function of a skydiver if you know the acceleration due to gravity?
• What role does air resistance play in setting up integrals for a skydiver's motion?
• Explain how the Fundamental Theorem of Calculus applies to finding the position of a skydiver at any time t.

Related terms

Velocity Function: Function that describes the rate of change of position with respect to time. It is found by integrating the acceleration function.

Acceleration Function: Function that describes the rate of change of velocity with respect to time. For a falling object, it often includes gravitational acceleration and air resistance.

Fundamental Theorem of Calculus:

\( \text{Links differentiation and integration; states that if } F(x) \text{ is an antiderivative of } f(x), \text{ then } \int_a^b f(x) \, dx = F(b) - F(a). \)