Scalar Diagram (involving distances only):

math expression

We can see that:

`sin\ theta=5/x`, so


Vector Diagram (involving velocities):

Related rates winch problem

[See the section on Vector concepts for more on vectors and scalars.]

We are also given that:

`(dx)/(dt)=-2\ "ms"^-1`

Since we need `(d theta)/(dt)`, we use:

`(d theta)/(dt)=(d theta)/(dx)(dx)/(dt)`



we have:

`(d theta)/(dx)=1/(sqrt(1-(5/x)^2))(d(5/x))/(dx)`



`(d theta)/(dt)=(d theta)/(dx)(dx)/(dt)`



We want to know the rate of change of θ when x = 10 m, so we substitute, as follows:

`(d theta)/(dt)=10/(10^2sqrt(1-(5/10)^2))`

`=0.1155\ "rad"//"s"`

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