As shown below, a cart weighing 300 N loaded with 500 N of coal was rolling along a track with almost no friction. A child on a bridge 10 m above the track thought it would be fun to drop something into the cart. The child's timing was perfect, and a 5 kg sack of flour fell straight down into the cart and broke open upon impact. Flour went everywhere and coated the coal so that it looked like the cart was carrying a load of chalk. What was the effect on the velocity of the cart?

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)