related rates

  1. MarkFL

    Lesson Related Rates: Lighthouse Beam

    A lighthouse is fixed \(y\) units from a straight shoreline. A spotlight in the lighthouse revolves at a rate of \(R\) revolutions per minute, shining a spot along the shoreline as it spins. At what rate is the spot moving when it is along the shoreline \(x\) units from the shoreline point...
  2. MarkFL

    Lesson Related Rates: A Sand Pile

    Sand is being dumped from a conveyor belt at a constant rate, forming a conical pile. The ratio of the base radius of this pile to its height is constant. Find the height of the pile as a function of time. To begin this problem, let's define some constants: \(a\) = the rate at which sand is...