Problem 1: You are standing at the edge of a slow-moving river, which is one mile wide, and wish to return to your ground on the opposite side of the river. You will swim at 2 mph and walk at 3 mph. You must first swim across the river to any point on the opposite bank. From there walk to the ground, which is one mile from the point directly across the river from where you start your swim.
What route will take the least amount of time?
Problem 2: A cylindrical can is to hold 20 m3. The material for the bottom and top costs $10/m2 and material for the side costs $8/m2. Evaluates the radius r and height h of the most economical can.
Problem 3. Show that an equilateral triangle provides the most area for a fixed perimeter.
Problem 4. The sides of an equilateral triangle are decreasing at a rate of 4 in/hr. How fast is the area enclosed by the triangle decreasing when the sides are 3 feet long?
Problem 5. What angle should my son aim his stomp rocket to get the maximum range? Justify your answer using methods from this class.
Problem 6. If he sets the launcher on a chair and goes for maximum range, how high will it go and at what time will it hit its apogee?