Suppose a ball is thrown straight up with initial velocity vo at time t = 0 from height h. The acceleration due to gravity is given as g. The motion occurs

over 7 equally spaced instants in time. The ball reaches its highest point ymax at time t = t3. The ball comes back to height h at t = to and hits the ground at time t = t7. a. (5 points) Sketch a motion diagram for the ball. Clearly define and label a coordinate system used for analyzing the motion. List and define/describe any physical assumptions you will be making to analyze the motion. Clearly label your diagram with any relevant information from the problem statement. To make your diagram easier to interpret, it may help to split it into multiple parts: the upward motion and the downward motion. b. (5 points) Sketch a graph of the object's acceleration as a function of time a(t). Clearly label your sketch with relevant information from the problem statement. c. (5 points) Sketch a graph of the object's velocity as a function of time v(t). Clearly label your sketch with relevant information from the problem statement. Make sure that the time axis of your velocity graph aligns with the time axis of your acceleration graph. d. (5 points) Sketch a graph of the object's position as a function of time y(t). Clearly label your sketch with relevant information from the problem statement. Make sure that the time axis of your position graph aligns with the time axis of your velocity and acceleration graphs. e. (5 points) Define a turning point of motion using words, symbols and diagrams. Clearly indicate where the turning points of motion are for the object on your graphs from parts a), b) and c).