## Archive for the ‘Navigation’ Category

### A Random Pursuit

Saturday, December 1st, 2007

A missile is launched when an airplane is directly overhead, at a height $h$. The missile moves at a constant speed $v$ always heading directly towards the aircraft, which is moving along a straight line at constant velocity $u$. What is the shape of the missile’s trajectory? How far will the aircraft fly before it is hit by the missile? What if the plane takes evasive action by randomly changing its direction, but heading in the original direction on the average? What is the best strategy for the missile to maximize the probability of a hit?

### Medieval Navigation in the Arabian Sea

Thursday, August 9th, 2007

Read First: Longitude Zero

Indians call the bay between Africa and India the Arabian Sea. Throughout the medieval times it was controlled by Arab sailors. They established settlements down the East coast of Africa, as far down as Malindi in Kenya. (more…)