1. Identify the Question One of the designers shows you that the proposed roller coaster will have a cart that is launched from ground level, sending it up a tall hill. The hill is going to be as tall as possible given the city's building code restraints. The team discusses the motion thev expect the coaster cart to have as it is launched and goes up the hill: C: Before the launch, it's sitting still. Then after the launch, it's moving really fast. A: Does it keep getting faster the whole time? Or does it slow down after the launch, when it goes up the hill? 3: Or, it could stav the same speed, after the launch and up the hill. There seem to be two different motions involved here: rst, the launch of the cart and second, the cart moving up the hill. Draw the motion diagram for the cart as it is launched. Draw the motion diagram for the cart as it travels up the hill. The first question the designers want to solve is, "What speed should the cart be launched at?" However, in order to answer the question, the designers (and you!) have to consider many related questions as well: . What's the acceptable range of launch speeds? . Should the cart just barely make it over the hill? How fast would the launch speed be to make that happen? . Should the cart go really fast over the hill? What's the fastest it should go, and how does that change the launch speed? . Does the launch speed depend on other physical factors that could change the design of the roller coaster itself? . Does the launch speed depend on how steep the hill is? . Does the launch speed depend on how many passengers are in the cart? Let's address the first set of questions: what is the acceptable range of speeds? If the launch is too fast, it'll be lots of fun (for the first moment), but might not be safe for a couple of reasons: there's a danger of the cart leaving the track at the top of the hill, and getting up to a very high speed in a short amount of time can have bad effects on the human body. However, if the cart launch is too slow, it'll be safer, but not only less fun, it might not even make it over the hill at all! The ideal launch speed should be somewhere between the two extremes. Finding the values of those extremes would let us determine the range of reasonable launch speeds. What about the second set of questions about other physical factors that might affect the speed? The shape or steepness of the track might matter-perhaps if it's really steep, the initial launch needs to be faster..or maybe that's true if the track is really long and shallow. Because this question is about the track, we'll get insight into how it affects the speed by investigating the interaction of the cart with the track. We can also investigate how the presence of people affects the cart's motion by looking at what happens with the mass of the cart is changed. The first question you'll investigate is: What launch speed would be the slowest possible, yet still allow the cart to make it to the top of the hill? QUESTION 1: If only the launch speed itself matters, will you need to care about the part of the motion when the cart is launched, or the part of the motion when the cart is traveling up the hill? Justify your