A fishing boat of mass m moves through water in the +x direction. At time t = 0, it is at location x = 0 and has speed v0 at that precise moment, the boat’s captain turns off the engines and lets the boat drift. Taking the drag force into account, Fd=-Kv^2, calculate the boats velocity as a function of time.
A sleek speedboat also passes the point x = 0 at time t = 0. Its speed at that moment is only half the fishing boat’s speed: v0/2. Now this super-sleek speedboat is designed so well that it experiences a negligible amount of drag: Fd=0 for the speed boat. Consequently, the speedboat’s captain doesn’t even
have his engines turned on! The fishing boat passes the speedboat, but eventually, the speedboat will catch up to the fishing boat. At what position X do the two boats meet? Write down a formula for X that is solvable and involves only known parameters. (Don’t try to solve it, it doesn’t have an analytic solution.)
The Attempt at a Solution
For part a I set the drag force equal to ma and solved it to be v(t)=v0-m/kt. I don't know if this is right but it makes sense to me, I have no idea how to approach part b though.