Related Rates
The Sliding Ladder
A ladder of length {{ L }}m is sliding down a wall. The bottom moves right at a constant speed. Notice how the vertical speed (blue arrow) changes!
Drag to slide
Link the Variables
Geometry relates the changing horizontal distance and vertical distance to the constant ladder length . Build the Pythagorean theorem.
Drag to build
Differentiate over Time
Take the derivative of each term with respect to time . Remember the Chain Rule: variables like are functions of !
Tap matching derivative
The Snapshot
Find how fast the ladder slides down () at the exact moment when .
Position
Rates
2
{{ problem.x }}
·
{{ problem.dxdt }}
+
2
{{ problem.y }}
·
= 0
Drag to substitute
{{ item.val }}
Solved!
Calculus Master!
You successfully linked the variables, took the derivative with respect to time, and solved for the unknown rate.