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 fixed horizontal position x=0. 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 y=h and speed v0, they consistently land on the ground on a target that is at a position x=d. positive directions for vector quantities are indicated in the figure.