The classic related rate problem of a shadow for a person walking away from a lamppost.[br]The lamp is 6 m tall and the person is 2 m tall.[br]The speed of the person (dx/dt) can be varied ( 1 to 3 recommended range ).[br]The second graph optionally shows the Distance of the person from the lamppost, the length of the Shadow and the distance of the shadow tip from the lamppost.[br]The play button in the lower left animates the time.

Derive an equation for the length of the shadow from the distance.[br][br]Take the derivative with respect to time.[br][br]Solve for the rate of increase of the shadow length from the speed of the person.[br][br]Does this equation match what you see in the lower graph?