(I) Kinetic energy #KE=1/2mv^2#,

where #m# is mass of object and #v# its velocity.

Kinetic energy of Allegheny class locomotive is given by, where given velocity has been converted to SI units

#KE=1/2(5.368xx10^5)(72.0xx10^3/3600)^2#

#=>KE=1.0736xx10^8J#

(II) Converting to CGS units,

#KE=1.0736xx10^8/4.184cal#

#=>2.568421xx10^7cal# .....(1)

Since it is steam engine as such we need to consider heat lost by

(1) steam at #100^@C# to become water at #100^@C#

(2) water for #DeltaT=75.0^@C#

Let #m# be water needed to provide required heat.

Heat lost in step (1) #Q_1=mL#

where #L=539calcdotg^-1# is latent heat of vaporization of water

#=>Q_1=539m" "cal#

Heat lost in step (2) #Q_2=msDeltaT#

where #s=1calcdotg^-1cdotK^-1# is specific heat of water.

#=>Q_2=mxx1xx75.0#

#=>Q_2=75.0m#

Total heat lost #=Q_1+Q_2=539m+75.0m=614m" "cal# .....(2)

Assuming that there is no loss of heat and all lost heat is converted in the kinetic energy, equating (1) and (2)

#614m=2.568421xx10^7#

#=>m=(2.568421xx10^7)/614#

#=>m=4.183xx10^4g#