Writing equations for rate of change problems

[Poppynz]

Hi
Im trying to write an equation for the question below. i did write one but am pretty sure it is wrong because I need to differentiate arctan in it and we have not been taught that yet. Could someone please point me in the right direction with writing it?

Homework Statement

A telescope is 75m above water level on a cliff and a boat is approaching at 6m/s. what is the rate of change of angle of the telescope when the boat is 75m from shore.

Homework Equations

The Attempt at a Solution

I thought it might be y=arctan(75/x) because the angle specified is found using arctan(opposite/addjacent).

Any suggestions appreciated :)

 

[tiny-tim]

… I thought it might be y=arctan(75/x) because the angle specified is found using arctan(opposite/addjacent).

Any suggestions appreciated :)

Hi Poppynz!

Just write it tanθ = 75/x, and differentiate both sides wrt x …

from the chain rule, you'll get a sec²θ, which you can rewrite in terms of the original 75/x

 

[Poppynz]

Thanks that seems much easier :)