Suppose a ship is searching visually for a life raft and that at time t, range is r(t) and detection rate is
gamma(t) = 40 / r(t)^3 hr^-1,
with t in hours, and r(t) in nm. The ship starts the search at an initial range of 2 nm and approaches the life raft on a direct course at a speed of 10 knots. Answer the following:
a. What are r(t) and gamma(t)?
b. What is the probability that detection will occur before the range decreases to 1 nm?
a. We have r(0) = 2 nm and v(t) = 10 nm/hr, so
r(t) = r(0) - vt = 2 - 10t,
where r is measured in nm and t in hours.
b. The detection rate is given by
gamma(t) = 40/r(t)^3 = 40/(2 - 10t)^3 = 5/(1 - 5t)^3.
Therefore the expected number of detections by the ...
This solution computes the probability that an incoming ship will rescue a lifeboat, using Poisson statistics.