The collision between a hammer and a nail can be considered to be approximately elastic. Estimate the kinetic energy acquired by a 10-g nail when it is struck by a 550-g hammer moving with an initial speed of 3.8 m/s.
I disagree with your premise, if that were true, nails would not get hot when struck.
Momentum conservation:
550*3.8=550Vh' + 10Vn'
Vh'=3.8-1/55 3.8Vn'
energy conservation
1/2 550*3.8^2=1/2 550 Vh'^2 + 1/2 10 Vn^2
put the Vh' expression found into this equation, do the math, solve for Vn'.