A temperature probe with a recovery factor r $=0\mathrm{.}75$ is used to measure the static

temperature of the air outside an airplane flying at $7000$ m with a speed of $270$ m$/$s$.$ Local

atmospheric pressure at $7000$ m is $45$ kPa, which results in an air density of $0\mathrm{.}66$ kg$/$m$3.$

a$)(5$ pts$)$ If the probe indicates a temperature of $7\mathrm{.}5$C$,$ what is the actual static air

temperature? Take cp $=1000$ J$/$kg $$ K$.$

b$)$ Concept question: $(5$ pts$)$ Discuss additional factors that might affect the accuracy of

the static temperature reading.

$3.(10$ pts$)$ A $0-$to$-10$ V$,4-$bit successive approximation A$/$D converter is used to measure an

input voltage.

a$)(3$ pts$)$ Determine the quantization error of the A$/$D converter.

b$)(3$ pts$)$ For an analog voltage input of $2\mathrm{.}9$ V$,$ determine the binary representation and

corresponding digital output voltage.

c$)(4$ pts$)$ What number of bits would the A$/$D converter need to ensure a reading within

$2\mathrm{.}5$ mV of the actual output voltage?