Motion System Design

# Fun With Fundamentals: Problem 185

Intercept course and Solution to Problem 184. The shortest path between two points of interest is not always a straight line, as this problem by F.O. Underwood of Sacramento demonstrates

Intercept course

Problem 185 — The shortest path between two points of interest isn’t always a straight line, as this month’s problem by F.O. Underwood of Sacramento demonstrates. It was half an hour before the grand opening of Hollywood’s newest and most fashionable restaurant, Chez Pfui, and proprietor Finagel J. Wurme, newly released from prison, was anxious for a success. He had invited the three top stars from the latest box-office smash, “Flopp: The Movie,” and was counting on the publicity. The doors would open at noon exactly, and everyone’s entrance had been carefully choreographed by experts at one of the leading studios. Several highly discreet rehearsals had taken place. The restaurant was set somewhat near the center of a large, square park. There were straight, level walkways from each of the four corners of the park to the restaurant. Each of the stars was to saunter up a different walkway, arrive simultaneously at the front door at noon, and express surprise at seeing one another.

Wurme would also be sauntering up one of the walkways and would express appropriate delight at seeing such luminaries in his humble establishment. He was also timed to arrive at noon.

The choreographers had it down to perfection. Alison, starting from the northeast corner, would leave at 11:55. Bobbi, who would take the path from the southeast corner, would depart at 11:56, and Charlene, from the southwest corner, would start at 11:57. Wurme was to start from the northwest corner.

Suddenly Wurme had an idea. Why not be seen on the arm of one of the stars? He chose Charlene, because her green outfit would match his green tie. Mindful of the cameras waiting at the door, Wurme did some arithmetic. He would need time to walk over to Charlene’s corner before she started. With a chuckle he timed his departure for 11:55.

Assume everyone walks at the same rate and neglect the size of the restaurant in your diagram. Did Wurme miscalculate? Will the photographers catch Wurme side-by-side with Charlene or single file?

Fun With Fundamentals
POWER TRANSMISSION DESIGN
1100 Superior Ave.
Cleveland, OH 44114-2543

Deadline is August 10. Good luck!

Technical consultant, Jack Couillard, Menasha, Wis.