# Calculus Problems Related Rates

Complicated calculus problem – related rates?

Hey calc freaks, I’m having some trouble with this question…

The top of a 5 m wheeled ladder rests against a vertical wall. If the bottom of the ladder rolls away at 1/3 m/s, how fast is the top of the ladder sliding down the wall when it is 3m above the base of the wall?

Thanks!

a=4
da/dt=1/3
b=3
db/dt=?
c=5
dc/dt=0, c is constant

using pythagorean theorem
a=4

a²+b²=c², take the derivative with respect to time
2a(da/dt) + 2b(db/dt) = 2c(dc/dt)
2(4)(1/3)+2(3)(db/dt)=2(5)(0)
8/3 + 6(db/dt)=0

db/dt= 4/9 m/s

How to solve related rate calculus word problems

Category: Calculus Problems
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