Related Rates Problem

Question

A 5ft ladder is resting against a wall. The bottom of the ladder is being pushed towards the wall at the

rate of 3 ft/sec. How fast is the top of the ladder moving up the wall when the bottom is 3 ft away from

the wall?

Answer 1

x is the measure from the bottom of the ladder to the wall

y is the measure from the top of the ladder to the ground

x^2 + y^2 = 5^2 = 25

2 x dx/dt + 2 y dy/dt = 0

x dx/dt + y dy/dt = 0

When x=3, 3^2 + y^2 = 25

9 + y^2 = 25

y^2 = 16

y = 4

(3)(3) + 4( dy/dt) = 0

9 + 4 dy/dt = 0

4 dy/dt = -9

dy/dt = -9/4