Question

The story is told about the sergeant who stopped at the jewelry store every morning at nine oclock and compared and reset his watch with the chronometer in the window. Finally, one day the sergeant went into the store and complimented the owner on the accuracy of the chronometer.

"Is it set according to time signals from Arlington?" asked the sergeant.

"No," said the owner, "I set it by the five oclock cannon fired from the fort each afternoon. Tell me, Sergeant, why do you stop every day and check your watch?"

The sergeant replied, "Im the gunner at the fort!" Is the feedback prevalent in this case positive or negative? The jewelers chronometer loses two minutes each 24-hour period and the sergeant9;s watch loses three minutes during each eight hours. What is the net time error of the cannon at the fort after 12 days?

Answer 1

The feedback in this case is negative, and the net time error of the cannon at the fort after 12 days is 84 minutes.

Step-by-step explanation:

In this case, the feedback is negative. The jewelers chronometer loses two minutes each 24-hour period, and the sergeant's watch loses three minutes every eight hours. The cannon at the fort, which the sergeant used to set his watch, will have a net time error after 12 days. To calculate this, we need to find the total time error of both the chronometer and the watch over 12 days, and then subtract them from each other. The chronometer loses 2 minutes per day, so over 12 days, it will lose 24 minutes. The watch loses 3 minutes every 8 hours, so over 12 days, it will lose (3 minutes x 3 times per day x 12 days) = 108 minutes. Therefore, the net time error of the cannon at the fort after 12 days is (108 minutes - 24 minutes) = 84 minutes.