Question

A 5-meter ladder leans against a wall. Suppose that the top is sliding down the wall at a rate of 1.2 m/s. calculate dx/dt when h=3m.

Answer 1

key equation

pythagorean theorem
\[a^2+b^2=c^2\]

Answer 2

if that still doesnt help, i suggest drawing a picture

Answer 3

so it would be \[a ^{2} +3^{2} =5^{2}\]??
and then take the derivatives?

Answer 4

nope
dont substitute the 3 in yet

Answer 5

x^2+y^2=5^2

move the y or x to the other side

x^2=25-y^2

then you take the derivative with respect to time

dx/dt would be the rate x is increasing
dy/dt would be the rate y is increasing

Answer 6

anyways if you take the derivative with respect to time for
x^2=25-y^2

what would you get?

Answer 7

2x=25-2y

Answer 8

?

Answer 9

close, but you're taking the derivative with respect to t
x and y are lengths,
you would get

2x(dx/dt)=-2y(dy/dy)

also the derivative of a constant is 0, so there wouldnt be a 25

Answer 10

what we know

top is sliding down at a rate of 1.2 m/s
so
dy/dt =-1.2 m/s
we want to solve for dx/dt when h=3

so y=h=3

you can determine x from pythagorean theorem

so all you need to do is solve for dx/dt