RR: Light and Shadow
The classic related rate problem of a shadow for a person walking away from a lamppost. The lamp is 6 m tall and the person is 2 m tall. The speed of the person (dx/dt) can be varied ( 1 to 3 recommended range ). 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. The play button in the lower left animates the time.
Derive an equation for the length of the shadow from the distance. Take the derivative with respect to time. Solve for the rate of increase of the shadow length from the speed of the person. Does this equation match what you see in the lower graph?