Consider vases of various shapes being filled with water at a constant rate. Cylindrical vase Spherical vase a. (3 points) For each vase, sketch a graph of time vs. volume as it is being filled. b. (3 points) For each vase, sketch a graph of time vs. height of the water in the vase as it is being filled. Elliptic paraboloid vose c. (3 points) For each vase, sketch a graph of the height of the water in the vase vs. the volume of the water in the vase. d. (1 point) How did you decide to the appropriate values for time in the graphs you sketched in parts (a) and (b)? e. (1 point) In part (c), what is the role of time in the sketch you provided? dfA 2. (5 points) You are driving in the vicinity of city A and city B. Secret Agent Cody's dispatcher is keeping track of the distance your car is from city A vs. the distance your car is from city B. Draw a path your car would have to take in order for the dispatcher to see what is shown in Figure 2. Sketch this and include any important points or directional markings. dfB City A City B Note that a qualitative sketch showing important points is sufficient (i.e. determining formulas to produce the sketch is not necessary). (4 points) We drop a basketball from a height of 2 meters and keep track of its height above the ground with respect to time. Our recording device produces the graph given below. Height vs. Time Y (m) 2.0 1.5 1.0 0.5 0.0 Time (e) Graph of basketball's height above the ground vs. time Create a sketch of the distance traveled by the ball vs. the distance above the ground.