Hard Calc Related Rate Problem
An outfielder throws the ball toward home plate with an initial velocity of 100ft/sec towards home plate, which is 300 feet away. An infielder positions him in a direct line between the outfielder and home plate. The infielder, who can throw the ball with an initial velocity of 110 ft/sec, can position himself x feet from home plate, at which he can, if he chooses, catch the ball and relay it towards home plate. Let R be the amount of time necessary for the infielder to make the relay to home plate. Due to air resistance, the velocity v(t) of the thrown ball satisfies the differential equation dv/dt = =v/10. Ignore vertical motion to answer the following.
a.Express the time T for the ball to reach home as a function of R and x.
b. Minimize T through an appropriate choice of x.
c. How fast must the relay be made in order to make it advisable?
I have no idea how to even start this.