Student Resources
Related Rates: Shadow
As Bob walks away from a lamp post at a brisk rate of 2 m/s, he notices that his shadow seems to be getting longer at a constant rate. You can explore Bob's motion and its relationship to his shadow's length in the applet below. Note, for the following problems you do not need to know the height of the lamp post or Bob's height.
Click "Walk" to see him walk at a speed of 2 m/s.
Click "Stop" then drag the dot below him to move him to any position you want.
Drag the scale slider to view either more detail or more distance.
Click ⛶ to open in full screen
When Bob's distance from the lamp post increases by an amount \(\Delta x\), the length of his shadow increases by a corresponding amount \(\Delta s\). Use the applet to determine the relationship between these changes as Bob walks away from the lamp post.
As Bob walks away from the lamp post at a rate of 2 m/s, how fast is the length of his shadow increasing?
Let \(x\) be the distance from Bob to the lamp post and \(s\) be the length of his shadow, both in meters. Bob is \(B\) meters tall and the lamp post is \(L\). meters tall. Write an equation relating \(x\) and \(s\). It does not need to be solved for any particular variable.
Let \(x\) be the distance from Bob to the lamp post and \(s\) be the length of his shadow, both in meters. Bob is \(B\) meters tall and the lamp post is \(L\). meters tall. Write an equation relating \(\displaystyle\frac{dx}{dt}\) and \(\displaystyle\frac{ds}{dt}\).