Related Rates Question

Question

5) A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?

Answer 1

The set-up will look something like this:

 

light

 |

 |

 | 20 ft                     |

 |                        7 ft|

 |________________|___________

            x                     L 

 

The picture will look something like this.  You will have to imagine the hypotenuse going from the light to the ground.

 

We have similar triangles.  So

 

20           =    7  

x + L             L

 

Cross multiplying gives 20L = 7(x +L)

 

Now what?  Hint:  You have been studying ???  Derivatives?   So take the derivative.  Do you suppose you need implicit differentiation?  You will need two different RATES that are RELATED by some equation containing them both.

 

The question is - how fast is L changing.