Question

the wheels of the locomotive of a train are 2.1m in radius.they make 75 revolutions in one minute . find the speed of the train in km pr hour.

Answer 1

Since the wheel makes 75 rev/min, the outside (circumference) of the wheel travels along the ground 75 times in one minute. Thus you need to know the circumference or the distance around the outside of the wheel. 

You know that the circumference of a circle is equal to 2 times pi times the radius, or 
C = 2 π r or 
C = 2 * π * (2.1) 

Using 3.14 for π, 

C = 2 (3.14)(2.1) or C = 13.2 meters (depending on how you are to round your answers...) 

Since the wheel goes around 75 times per minute, the wheel will travel approximately 990 meters per minute. 

In an hour (60 minutes) the train will travel 990(60) meters, or about 59400 meters. 

Converting this to km, the train will travel approximately 59.4 km/hr

Answer 2

Hello !
The radius of the wheel (r) = 2.1 m
No. of revolutions in one minute = 75
no. of revolutions per second (n) = 75/60 = 15 / 12 = 5/4 revolutions
The distance traversed in one second (Speed) = 2πr × 5/4 = 13.2 × 5/4 = 16.5 m/sec
Speed in km/h = 16.5 × 18/5 =  59.4 km/h 
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