Composite functions to model extraterrestrial skydiving

TL;DR

This video explains how to model Flox's terminal velocity using the width of her parachute and evaluates it when the parachute is 14 meters wide.

Transcript

• [Instructor] We're told that Flox is a skydiver on the planet Lernon. The function. A of w is equal to 0.2 times W squared, gives the area, A, in square meters under Flox's parachute when it has a width of W meters. That makes sense. The function V of A is equal to the square root of 980 over A gives Flox's maximum speed in meters per second when... Read More

Key Insights

• 🪂 Flox's parachute area can be determined using the function A(w) = 0.2w^2.
• 🐎 The function V(A) = √(980/A) calculates Flox's maximum speed based on the parachute area.
• ❓ Terminal velocity can be modeled using V(A(w)) = √(980/(0.2w^2)).
• 🤒 The width of 14 meters yields a terminal velocity of 5 meters per second for Flox.
• 🪂 Terminal velocity depends on the width of the parachute.
• 😑 The calculation involves substitution of the width into the modeled expression.
• 🐎 Flox's terminal velocity is the maximum speed reached while skydiving.

Questions & Answers

Q: How can Flox's parachute area be represented mathematically?

Flox's parachute area is represented by the function A(w) = 0.2w^2, where w is the width of the parachute in meters. This equation gives the area in square meters.

Q: What is the function V(A) used for?

The function V(A) = √(980/A) is used to calculate Flox's maximum speed in meters per second when skydiving with an area A square meters under her parachute.

Q: How can Flox's terminal velocity be modeled using the width of her parachute?

Flox's terminal velocity as a function of her parachute width can be modeled using V(A(w)), which is equal to √(980/(0.2w^2)). This equation combines the functions A(w) and V(A).

Q: What is Flox's terminal velocity when her parachute is 14 meters wide?

To find Flox's terminal velocity when her parachute is 14 meters wide, we evaluate the expression V(A(w)) with w = 14. The calculation results in a terminal velocity of 5 meters per second.

Summary & Key Takeaways

• Flox's parachute area, A, in square meters is modeled by the function A(w) = 0.2w^2, where w is the width of the parachute in meters.

• The function V(A) = √(980/A) gives Flox's maximum speed in meters per second when skydiving with an area A.

• To model Flox's terminal velocity as a function of her parachute width, we use V(A(w)), which equals √(980/(0.2w^2)).