This question is a short free-response question. Show your work for each part of the question. x='0 x=g x'=D xe x2D A group of students prepare for a robotic competition and build a robot that can launch large spheres of mass M in the horizontal direction with a variable speed and from a variable vertical position and a xed horizontal position a: = U. The robot is calibrated by adjusting the speed at which the sphere is launched and the height of the robot's sphere launcher. Depending on where the spheres land on the ground, students earn points based on the accuracy of the robot. The robot is calibrated so that when the spheres are launched from a vertical position 3; = H and speed on, they consistently land on the ground on a target that is at a position a: = D. Positive directions for vector quantities are indicated in the gure. (a) 0n the axes below, sketch the graphs of the horizontal and vertical components of the sphere's velocity v as a function of time it between t = 0, when the sphere is launched and t = T, when the sphere hits the target. Label t = Tforthe horizontal component of the sphere's velocity and the vertical component of the sphere's velocity. Horizontal Component of Spheres Velocity Vertical Component of Sphere's Velocity vs V .V When the students arrive at the competition. it is determined that the height of the sphere launcher can no longer be adjusted due to a mechanical malfunction. Therefore. the spheres must be launched at a vertical position of y = %. However, the spheres may be launched at speed on or 2v\". (b) In a clear, coherent paragraph-length response that may also contain diagrams andfor equations, describe the speed at which a sphere should be launched so that the students earn the maximum number of points in the competition