# Rate Of Change (derivatives) Word Problem

## Homework Statement

A 1.8 m tall student is trying to escape from the minimum security prison in To no.
She runs in a straight line towards the prison wall at a speed of 4.0 m/s. The guards
shine a spotlight on the prisoner as she begins to run. The spotlight is located on
the ground 30 m from the wall. At which rate is the prisoner's shadow on the wall
decreasing when she is 20 m from the wall?

## Homework Equations

All basic differentiation rules.

## The Attempt at a Solution

This is my problem, I know how to do derivatives fine, I can't set up the equation based on the information given, I was wondering if anyone could give me clues on how to set it up?

tiny-tim
Homework Helper
welcome to pf!

hi nexxia! welcome to pf! I know how to do derivatives fine, I can't set up the equation based on the information given, I was wondering if anyone could give me clues on how to set it up?

first you need to write out the equations for where everything is at a fixed time t …

what do you get? hi nexxia! welcome to pf! first you need to write out the equations for where everything is at a fixed time t …

what do you get? Do you mean manipulating v=d/t to make things equal to t and then make them equal to eachother?
going out on a limb here;
like t=d/v= 20m/4m/s ???

tiny-tim
Homework Helper
Do you mean manipulating v=d/t to make things equal to t and then make them equal to eachother?
going out on a limb here;
like t=d/v= 20m/4m/s ???

uhh? just write out the equations for where the prisoner is, and where the shadow is, at any fixed time t uhh? just write out the equations for where the prisoner is, and where the shadow is, at any fixed time t I dont know how do do that tiny-tim