Which of the following products of ratios gives the conversion factors to conver

Question

Which of the following products of ratios gives the conversion factors to convert meters per second (m/s) to miles per hour (mi/h)? 5 280 f/mi middot 12 in/f middot 2.54 cm/1 in middot 100cm/1 m middot 3 6000 s/1h 5 280 f/mi middot 12 in/f middot 1 in./2.54 cm middot 1 m/100 cm middot 1h/3 600 s 5 280 f/mi middot 12 in/f middot 2.54 cm/1 in middot 100cm/1 m middot 1h/3 600 s 1mi/5.280 f middot 1 f/12 in middot 1 in/2.54 cm middot 100cm/1 m middot 3 6000 s/1h 1 mi/5.280 f middot 1 f/12 in middot 1 in/2.54 cm middot 1 m/100 m middot 3 6000 s/1h A rocket, initially at rest, is fired vertically with an upward acceleration of 10 m/s^2. At an altitude of 0.50 km, the engine of the rocket cuts off. What is the maximum altitude it achieves? Free Fall Problem 1.9 km 1.3 km 1.6 km 1.0 km 2.1 km

Explanation / Answer

a. No.

[5280 f/mi][12 in/f][2.54 cm/in][100 cm/1 m][3600 s/h] = 5.7936384e+10 cm2.s/m.h

b. No.

[5280 f/mi][12 in/f][1 in/2.54 cm][1 m/100 cm][1 h/3600 s] = 6.93e-2 in2.m.h/mi.cm2.s

c. No.

[5280 f/mi][12 in/f][2.54 cm/ 1 in][100 cm / 1 m][1 h/3600 s] =4.47e+3 cm2.h/mi.m.s

d. Yes.

[1 mi /5280 f][1 f/ 12 in][1 in /2.54 cm][100 cm / 1 m][3600 s/ 1 h] = 2.237 mi.s/m.h = 2.237 (mi/h)/(m/s)

e. No.

[1 mi /5280 f][1 f/ 12 in][1 in /2.54 cm][1 m/100 cm][3600 s/ 1 h] = 2.237e-4 mi.m.s/cm2.h   

answer: option (d) is correct answer.

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