MATLAB Exercises Exercise M1 Consider the situation below, in which two carts, traveling along the same straight line, collide elastically. 30cm/s 20cm/s 270g 120g (a) What are the final velocities of the two carts? (b) Check your answers fully by verifying that two physical principles are satisfied Look up the equations for one-dimensional elastic collisions on the web or in a physics text. You are looking for an expression for the final velocity of each cart in terms of the four values given in the diagram. In other words, you are not expected to derive the equations you need. Make sure to include a citation near the top of your MATLAB script telling me the source you used. There is no reason to convert the given values to MKS units. You should leave them in g and cm/s. You should call the cart on the left "Cart #1" and the cart on the right "cart #2" For a robust script, use variables to define the given values, then use these variables throughout the rest of your script. You should find that there is a factor that is repeated multiple times. Define a new variable so that you don't need to compute it so many times. (And remember to suppress output when you define it, as it does not answer a question.) You may also consider simplifying your expressions by pulling out any common factors. For part (b), once you have computed values for the final velocities, develop two checks, one fo each physical principle that is used to derive the equations you looked up. Note that a proper check is designed to be equal to zero, if at all possible. (Extremely small numbers, e.g., 10-13, are remnants of floating point errors in the calculation. We interpret them as zero.)