Final answer:
To find the speed of the train in km per hour, first calculate the angular velocity in radians per second. Then, multiply the angular velocity by the radius of the wheels to find the linear velocity. Finally, convert the linear velocity from meters per second to kilometers per hour.
Step-by-step explanation:
To find the speed of the train in km per hour, we need to convert the linear velocity of the train from meters per second to kilometers per hour. Given that the wheels of the locomotive have a radius of 2.1 m and make 75 revolutions in one minute, we can calculate the linear velocity of the train using the formula v = rw, where v is the linear velocity, r is the radius of the wheels, and w is the angular velocity in radians per second.
First, we find the angular velocity by converting the number of revolutions per minute to radians per second. One revolution is equivalent to 2π radians, so 75 revolutions is equivalent to 75 * 2π radians. Dividing this by 60 seconds gives us the angular velocity w in radians per second.
Once we have the angular velocity, we can calculate the linear velocity by multiplying it by the radius of the wheels. Finally, we can convert the linear velocity from meters per second to kilometers per hour by multiplying it by 3.6. The final result will give us the speed of the train in km per hour.