Related Rates and Shadow Problems

This video tutorial covers a classic related rates problem from the 1991 AP Calculus exam. The problem involves a tightrope walker illuminated by a spotlight, and the task is to determine the speed of the shadow on the ground and its movement up a building. The instructor explains the setup, uses similar triangles to find relationships, and solves the problem step-by-step, highlighting key concepts in related rates and geometry.

What year is the AP Calculus problem from?

• 1975

• 1985

• 2001

• 1991

How far apart are the J and T buildings?

• 100 feet

• 70 feet

• 50 feet

• 30 feet

At what constant rate is the tightrope walker moving?

• 4 feet per second

• 3 feet per second

• 2 feet per second

• 1 foot per second

How high above point A is the spotlight?

• 30 feet

• 100 feet

• 50 feet

• 70 feet

What is the main mathematical concept used to solve the problem?

• Integration

• Related Rates

• Limits

• Differentiation

What is the rate at which the shadow moves along the ground when the walker is midway?

• 10/7 feet per second

• 15/7 feet per second

• 20/7 feet per second

• 25/7 feet per second

How far from point A is the walker when her shadow reaches the base of the T building?

• 40 feet

• 25 feet

• 30 feet

• 35 feet

What happens to the shadow after it reaches the base of the T building?

• It moves up the building

• It disappears

• It stays at the base

• It moves back to point A

At what rate does the shadow move up the building when the walker is 10 feet from point B?

• 45/8 feet per second

• 40/8 feet per second

• 35/8 feet per second

• 30/8 feet per second

What is the key takeaway from solving this related rates problem?

• Understanding integration

• Visualizing geometric relationships

• Applying limits

• Memorizing formulas