Which of the following products of ratios gives the conversion factor to convert

Question

Which of the following products of ratios gives the conversion factor to convert miles per hour (mi/h) to meters per second (m/s)? 5280 f/mi middot 12 in/f middot 1 in/2.54 cm middot 1m/100 cm middot 1h/3600 s b. 5280 f/mi middot 12 in/f middot 2.54 cm/1 in middot 100 cm/1 m middot 1h/3600 s c. 1 mi/5280 f middot 1 f/12 in middot 1in/254 cm middot 100 cm/1 m middot 3600 s/1 h d. 5280 f/mi middot 12 in/f middot 2.54 cm/1 in middot 1 m/100 cm middot 1h/3600 s e. 5280 f/mi middot 12 in/f middot 2.54 cm/1 in middot 1 m/100 cm middot 3600 s/1 h A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity. The speed of the ball as see a stationary observer in the street: a. is less than that observed inside the bus. b. is the same as that observed inside the bus. c. is greater than that observed inside the bus. d. may be either greater or smaller than that observed inside the bus. e. may be either greater, smaller, or equal to that observed inside the bus.

Explanation / Answer

19. Option d is correct. All you need to do is check what units are remaining after the conversion. As you can see in option d, units remaing are mile/h x( h/mile x m/s) = m/s, which is the required unit.

20. Here speed, and not the velocity, is compared. Velocity will be smaller but speed, which is the magnitude of velocity, can either be greater or smaller or even equal. Hence option e is correct.

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