- Optimization problem ( 15 points)
A person in a rowboat y miles from the nearest point on a straight shoreline wishes to reach a house x miles farther down the shore.
The person can row at a rate of 3 mi/h and walk at a rate of 5 mi/h.
Make a user VBA form in which the user provides x and, y and the form:
a) Finds the least amount of time required to reach the house.
b) How far from the house, should the person land the rowboat?
Hint: This an optimization problem, that can be solve with calculus by:
I. writing the function to optimize in terms of only one variable,
II. deriving this function,
III. making the derivative equal to zero to find the critical point
IV. Calculating the second derivative to characterize the critical point as either minima or maxima
V. Substituting the critical point into the original function to solve the problem
- Stoichiometry (15 points)
Calcium carbonate reacts with hydrochloric acid to form calcium chloride, carbon dioxide, and water according to the following chemical reaction:
CaCO3 + HCl CaCl2 + CO2 + H2O (Unbalanced reaction)
In one reaction, x g of CO2 is produced.
Write a VBA-Excel form in which the user provides the x g of CO2 produced, and the form calculates the corresponding mass of CaCO3 and HCl reactants consumed and the mass of CaCl2 and H2O produced.
Hint: This is a stoichiometric problem, which can be solved by:
I. Balancing the chemical reaction
II. Calculating the number of moles of CO2 produced
III. From these number of moles of CO2, using the stoichiometric coefficients of the balanced reaction, calculate the number of moles, and then the masses of the other chemicals in the reaction.