2. Imagine that you are driving down a stretch of freeway with aposted speed limit of 65 miles per hour. You arenât sure whether totrust your speedometer, so you check your speed against a series ofdistance markers along the interstate. You notice that, in the timeit takes you to count to ten, you pass the 0.2 mile mark. Yourspeedometer, marked in intervals of 5 mph, reads 65 mph.
a. Are your speedometer and your measured speed the same to withinthe uncertainty of your measurements? Assume a ±0.5 s uncertaintyin your count; the mile markers have a 1% uncertainty in theirposition. Also recall the difference between standard deviation anduncertainty in the mean. [Note: DO NOT DO THIS ANALYSIS WHILEDRIVING!] Show all of your work.
b. You have just propagated the uncertainty in your ten secondcount through a series of calculations that involved multiplicationand then subtraction. (If this wasnât what you did, check yourwork!) You did this to test a hypothesis: that the speedometerreading was equal to your measured speed. Describe another,different situation where you might need to propagate theuncertainty through a series of simple calculations to test ahypothesis.
c. Letâs say that your uncertainty in your 10-second count was ±1%.Would you be able to tell that you were speeding? Show your workclearly and interpret your results.
d. Letâs say that your uncertainty in your 10-second count was ±1second. Would you be able to tell whether you were speeding? Showyour work clearly and interpret your results.
2. Imagine that you are driving down a stretch of freeway with aposted speed limit of 65 miles per hour. You arenât sure whether totrust your speedometer, so you check your speed against a series ofdistance markers along the interstate. You notice that, in the timeit takes you to count to ten, you pass the 0.2 mile mark. Yourspeedometer, marked in intervals of 5 mph, reads 65 mph.
a. Are your speedometer and your measured speed the same to withinthe uncertainty of your measurements? Assume a ±0.5 s uncertaintyin your count; the mile markers have a 1% uncertainty in theirposition. Also recall the difference between standard deviation anduncertainty in the mean. [Note: DO NOT DO THIS ANALYSIS WHILEDRIVING!] Show all of your work.
b. You have just propagated the uncertainty in your ten secondcount through a series of calculations that involved multiplicationand then subtraction. (If this wasnât what you did, check yourwork!) You did this to test a hypothesis: that the speedometerreading was equal to your measured speed. Describe another,different situation where you might need to propagate theuncertainty through a series of simple calculations to test ahypothesis.
c. Letâs say that your uncertainty in your 10-second count was ±1%.Would you be able to tell that you were speeding? Show your workclearly and interpret your results.
d. Letâs say that your uncertainty in your 10-second count was ±1second. Would you be able to tell whether you were speeding? Showyour work clearly and interpret your results.
