(a) A cheetah running at top speed of 60 mi/h; the local temperature is 40 degre

Question

(a) A cheetah running at top speed of 60 mi/h; the local temperature is 40 degrees C.

(b) A peregrine falcon in a dive at 217 mi/h; the local temperature is 25 degrees C.

(c) Maurice Greene, who in June 1999, in Athens, Greece, became the world's fastest human by running 100m in 9.79s; the temperature was 21 degrees C.

(d) Alexander Popov, who in June 1999 became the world's fastest swimmer by swimming 50m in 21.64 s; the temperature of the water was 20 degrees C.

2.14 Given the following speeds and temperatures, determine the corresponding Mach num- 0.447 m/s) 1.6093 km/h 1.609.3 m: 1 mi/h bers (Note: 1 mile 5,280 ft (a) A cheetah running at top speed of 60 mih; the local temperature is 40oC (b) A peregrine falcon in a dive at 217 milh; the local temperature is 25oC (c) Maurice Greene, who in June 1999, in Athens, Greece, became the world's fastest human by running 100 m in 9.79 s; the temperature was 21 C (d) Alexander Popov, who in June 1999 became the world's fastest swimmer by swim ming 50 m in 21.64 s; the temperature of the water was 20 C

Explanation / Answer

MACH NUMBER OF AN OBJECT = OBJECT SPEED / SPEED OF SOUND

a) SPPED OF SOUND AT 40deg C = 354.73 m/s

TOP SPEED OF CHEETAH = 60 mi/hr =60*1.6093*0.447= 43.16 m/s

MACH NUMBER = 43.16/354.73 = 0.1217

b) SPEED OF A PEREGRINE FALCON = 217 mi/hr = 217*1.6093*0.447= 156.1 m/s

SPPED OF SOUND AT 25deg C = 346.13 m/s

MACH NUMBER = 156.1/346.13 = 0.451

c) SPPED OF SOUND AT 21deg C = 343.801 m/s

SPEED OF MAURICE GREENE = 100/9.79 = 10.214 m/s

MACH NUMBER = 10.214/343.801 = 0.03

d) SPPED OF SOUND AT 40deg C = 343.216 m/s

SPEED OF ALEXANDER POPOV = 50/21.64 = 2.31 m/s

MACH NUMBER = 2.31/343.216 = 0.00067

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