An engine can move at the speed of 20/3 m/s with- out any wagon attached and reduction in the speed of the train directly proportional to the square root of the number of wagons attatched to the engine When there are 9 wagons attached its speed is 5 m/ s. The greatest number of wagons with which the engine can move is
Answers
Given : An engine can move at the speed of 20/3 m/s with- out any wagon attached and reduction in the speed of the train directly proportional to the square root of the number of wagons attached to the engine When there are 9 wagons attached its speed is 5 m/ s.
To Find : The greatest number of wagons with which the engine can move
Solution:
A locomotive engine without any wagons attached to it can run @20/3 m/s
Speed of locomotive = 20/3 - k√n
k is a constant
n - number of wagons attched
for n =9 speed = 5 m/s
=> 5=20/3 - k√9
=> 5/3 = 3k
=> k = 5/9
=> speed = 20/3 - (5/9)√n
The greatest number of wagons with which the engine can move is
=> speed > 0
=> 20/3 - (5/9)√n > 0
=> 60 - 5√n > 0
=> 12 - √n > 0
=> n < 144
143 number of Wagons
greatest number of wagons with which the engine can move is 143
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