Problem Statement | Two balls are next to each other rolling at identical speeds to the right on horizontal tracks. Track A remains horizontal the entire time. After traveling a distance of I1, track B has a dip with nearly vertical walls of height h. The bottom of the dip is horizontal and has a width w. The speed is slow enough that when ball B reaches the dip, it doesn't leave the track. We wish to explore which ball will reach the nish line rst. A l nEh (a) Let's start by deciding how the length I1 may affect who wins the race. Which ball travels the initial distance l1 rst? Explain your reasoning using any combination of words, diagrams, math, etc. (b) If you assume any speed gained while falling down into the dip is lost when the ball rolls back up the other side, ball B is traveling the same speed when it gets out of the dip as when it entered. If that's true, how may l2 affect which ball wins the race? Assume ball A rolls at a constant speed the entire time. Explain. (c) To think about the affect of the dip itself, lets use a special cases sensemaki'ng technique and make the dip very deep, h >> w\". Imagine the whole track being a few meters horizontally, but h is 100 m deep. Explain which ball would win the race and why. (d) Now use special cases sensemaking on the other extreme, imagine the dip width w >> h. If the whole track is a few meters horizontally, w is 90% of that and h is a few centimeters. Explain which ball would win the race and why. (e) What is your groups nal decision on who wins the race? Explain your reasoning using any combination of words, diagrams, math, etc