Motion System Design

Fun with Fundamentals: Problem 227

Problem 227 – Power meeting

July's problem, submitted by William Anderson of Brook Park, Ohio is relatively simple if you know the trick.

The Edisonville town council's emergency candlelight meeting was well into its second hour of debate when Professor R. L. Tivitee stepped up to the podium.

"People, we need to come to a decision. While fossil fuel and nuclear power are both fine sources of energy, they aren't nearly as efficient as antimatter. What's antimatter you ask? Why of course antimatter reacts on collision with an equal mass of normal matter to convert the total of the reacting masses into energy. For a small fee, I could set up a solarpowered, warp-speed, accelerometer. With the sunshine rate in Edisonville, it'll produce 20 mg of antimatter per day. This will solve our energy problems once and for all. If your projected power plant efficiency of 30% is correct, this will be more than adequate to produce the 100 MW that Edisonville requires."

Will the professor be able to turn this town on?

Solution to June’s Problem, 226:

You're batting 1.000 if you answered that the centerfielder would have to run in at an average speed of 3.2 m/sec. Here's how he made the play:

At 45°, the ball starts out with equal vertical and horizontal velocity components:

Vx = Vy (20m/ sec) cos 45° = (20)(.707) = 14.142m/sec

The vertical position as a function of time is:

For C = 0, there are two times when S=0: at t=0 (when the ball is hit) and at t=2.88 sec:

So, after 2.88 sec, the ball is at its original elevation and has traveled:

S = (2.88 sec)(14.142m/sec) = 40.77m

Thus, with the centerfielder starting at 50 m, he has to come in at:

9.23m ÷ 2.88 sec = 3.2m/sec

Here are the results

Fun problem 225
Shallow plot, May, 1999:

Total entries: 136
Number correct: 89 (65.4%)
Winner: Barry J. Hildebrand of
Rancho Palos Verdes, Calif.
Barry's prize: Maple V software

Special thanks to this month's problem submitter, William Anderson, of Brook Park, Ohio. He receives a Sharp EL- 546L scientific calculator.

Technical consultant: Jack Couillard, Menasha, Wis.