3. (a) An outfielder fields a baseball 280 ft away from homeplate and throws it directly to the catcher with an initialvelocity of 100 ft/s. Assume that the velocity v(t) of the ballafter t seconds satisfies the di↵erential equation dv dt = 1 10 vbecause of air resistance. How long does it take for the ball toreach home plate? (Ignore any vertical motion of the ball.)(Instructor’s hint: Recall that a di↵erential equation of the formdv/dt = kv has solution v(t) = v(0)ekt.) (b) The manager of theteam wonders whether the ball will reach home plate sooner if it isrelayed by an infielder. The shortstop can position himselfdirectly between the outfielder and home plate, catch the ballthrown by the infielder, turn, and throw the ball to the catcherwith an initial velocity of 105 ft/s. The manager clocks the relaytime of the shortstop (catching, turning, throwing) at half asecond. How far from home plate should the shortstop positionhimself to minimize the total time for the ball to reach homeplate? Should the manager encourage a direct throw or a relayedthrow? What if the shortstop can throw at 115 ft/s? (Instructor’shint: Let x represent the distance between the shortstop and homeplate, then find an expression for the time it takes that ball toreach home plate as a function of x. It is also helpful to use avariable w to represent the shortstop’s throwing velocity, sinceyou can then substitute the di↵erent given values in place of w.)(c) For what throwing velocity of the shortstop does a relayedthrow take the same time as a direct throw

Please answer part b