Rate of Change: How Fast is the Length of a Shadow Decreasing?

[jakealucard]

A man 1.8 m tall walks at speed of 10m/s towards a street lamp which is 7m above the ground. How fast is the length of the man's shadow decreasing?


My attempt:

Let the man's shadow and the lamp's length be l, and the distance be d and time be t. Given, dd/dt = 10.

I am supposed to find dl/dt.

dd/dt= dl/dt X dd/dl

So how do I find dd/dl?

 

[ahmadmz]

You can imagine the man walking on the x-axis towards the y-axis. Call his position x and the length of his shadow s.
The key to these types of problems is using similar triangles. So we can get a relation between s and x.

(1.8/s) = (7/x+s)

Get s on one side and differentiate with respect to t. And remember dx/dt = -10 since x is decreasing.

I hope i didn't make any mistake. Check the book to make sure if you have the answer.

 

[HallsofIvy]

Draw a picture and think "similar triangles".