1. The problem statement, all variables and given/known data A model land-yacht runs on a horizontal frictionless oval track as shown (viewed from above) in the figure. The curved parts of the track are semi-circles of radius R = 0:5 m; the straight sides have length L = 1 m. The mass of the yacht (including its sails) is m = 0:5 kg. A child plays with the toy by starting the yacht from rest at point A at the beginning of one of the straight segments of track (see diagram) and applying a force of mag- nitude jFj = 4N to the sails, using a fan as shown. The force is horizontal, directed at 30 (=6 radians) to the direction of the straight track (see diagram). Both the magnitude and direction of the force remain constant throughout the game. After passing B the yacht enters the curved section of the track on the right-hand side of the diagram. Find the maximum speed reached by the yacht on this curved section, and the angle (defined as shown) at which this maximum speed is attained. http://img856.imageshack.us/img856/8205/40514750.jpg [Broken] 2. Relevant equations Derived equations of motion F(centri) = mv^2/r 3. The attempt at a solution I've tried resolving along a line parallel to the line L, Fsin(theta) - 4cos30 = 0 and perpendicular Fcos(theta) - 4sin30 = 0 (I assumed the acceleration was zero because of the direction I was resolving in was not along the line of the acceleration). This had to be wrong as it just gave me theta = 30 and I also realised that the reaction force should have a role, but that would mean introducing an unknown force and angle which wouldn't allow me to find theta. I've thought about using polar unit vectors and work-kinetic theorem but I'm still running into unknown values. I'm a first year undergraduate. First post, I apologise if I've broken any rules. Thanks.