(a) A car speedometer has a 5.0%5.0% uncertainty. What is the range of possible speeds when it reads 90km/h90km/h ? (b) Convert this range to miles per hour. (1 km=0.6214 mi)
Question
(a) A car speedometer has a 5.0%5.0% uncertainty. What is the range of possible speeds when it reads 90km/h90km/h ? (b) Convert this range to miles per hour. (1 km=0.6214 mi)
Solution
(a) The uncertainty of the speedometer is 5.0%. This means that the actual speed of the car could be 5.0% more or less than the reading on the speedometer.
To find the range of possible speeds, we first calculate 5.0% of 90 km/h.
5.0/100 * 90 km/h = 4.5 km/h
So, the car's speed could be 4.5 km/h more or less than 90 km/h.
Therefore, the range of possible speeds is from (90 - 4.5) km/h to (90 + 4.5) km/h, or 85.5 km/h to 94.5 km/h.
(b) To convert this range to miles per hour, we multiply by the conversion factor of 1 km = 0.6214 mi.
85.5 km/h * 0.6214 = 53.1 mi/h 94.5 km/h * 0.6214 = 58.7 mi/h
So, the range of possible speeds in miles per hour is from 53.1 mi/h to 58.7 mi/h.
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