19. (a) if your speedometer has an uncertainty of 2.0 km/h at a speed of 90 km/h, what is the percent…

Explanation:

Step1: Calculate percent uncertainty for speedometer in 19(a)

Percent uncertainty formula is $\text{Percent Uncertainty}=\frac{\text{Uncertainty}}{\text{Measured Value}}\times100%$. Given uncertainty $\Delta v = 2.0\ km/h$ and measured value $v = 90\ km/h$. So, $\text{Percent Uncertainty}=\frac{2.0}{90}\times100% \approx 2.22%$.

Step2: Find range of speeds in 19(b)

First, since percent - uncertainty is the same ($2.22%$) and new measured value $v'=60\ km/h$. Uncertainty $\Delta v'=\text{Percent Uncertainty}\times v'$. $\Delta v'=\frac{2.0}{90}\times100%\times60\ km/h\approx 1.33\ km/h$. The range of speeds is from $v'-\Delta v'$ to $v' + \Delta v'$, so from $60 - 1.33=58.67\ km/h$ to $60 + 1.33 = 61.33\ km/h$.

Step3: Calculate percent uncertainty for blood - pressure in 20(a)

Using the percent - uncertainty formula $\text{Percent Uncertainty}=\frac{\text{Uncertainty}}{\text{Measured Value}}\times100%$. Given measured value $P = 120\ mm\ Hg$ and uncertainty $\Delta P=2\ mm\ Hg$. So, $\text{Percent Uncertainty}=\frac{2}{120}\times100% \approx 1.67%$.

Step4: Find uncertainty in blood - pressure in 20(b)

Since percent - uncertainty is $1.67%$ and new measured value $P' = 80\ mm\ Hg$. Uncertainty $\Delta P'=\text{Percent Uncertainty}\times P'$. $\Delta P'=\frac{2}{120}\times100%\times80\ mm\ Hg\approx 1.33\ mm\ Hg$.

Answer:

19(a): $2.22%$ 19(b): From $58.67\ km/h$ to $61.33\ km/h$ 20(a): $1.67%$ 20(b): $1.33\ mm\ Hg$