# Challenge 11 – Modeling Shadow Speed, Diameter and Duration along the Path of Totality

Problem 1 -  A simple function that predicts the speed of the lunar shadow in kilometers per hour is given by

V(L) = 1.06L2 +179 L +9900

where L is the longitude along the path.  This formula is accurate to about +/- 23 km/hr over the longitude range from -79 to -124 ( 79 West to 124 West)

A)        Does the speed ever reach zero across the continental United States?

B)        What is the longitude of the maximum speed of the shadow?

Problem 2 – A simple formula that predicts the diameter of the lunar shadow in kilometers is given by

D(L) = -0.0084L2 – 1.3423 L + 61.425

and is accurate to about 0.2 kilometers.  A) Does this function reach zero over the continental United States? B) At what longitude does it have its vertex and is this a maximum or a minimum value?

Problem 3 – The duration of totality is simply the time it takes the lunar shadow with a diameter of D kilometers to pass over the Observers location at a ground speed of V kilometers/hour.  A) From the functions in Problem 1 and 2, create the function T(L) which gives the duration of the eclipse in minutes. B) Graph this function over the longitude range from -124 to -79, which covers the continental United States. For what location will the eclipse last the longest?