Answer
$\Delta T=3675 C^{\circ}$
Work Step by Step
Essentially, the hammer will strike the nail, transferring its kinetic energy to the nail. Typically, the nail moves deeper wood, but the question assumes that the energy transferred will contribute to a rise in the temperature.
Starting off by the law of conservation of momentum, since the hammer is brought to rest:
$m_{hammer} \times v_{hammer}=m_{nail} \times\ v_{nail}$
Substituting in values, we get the speed of the nail to be:
$1.20kg \times 7.5ms^{-1}=0.014kg \times v_{nail}$
$v_{nail}=643ms^{-1}$
Thus, total kinetic energy transfer for 8 collisions would be:
$8 \times E_{k}=8 \times 0.5mv^{2}=Q$
$Q=4(0.014)(643^{2})$
$Q=23153J$
Given that the nail is an iron nail, using the referenced value in the chapter, iron has a specific heat capacity of 450J/kg
$Q=mc \Delta T$
$23153=0.014 \times 450 \times \Delta T$
$\Delta T=3675 C^{\circ}$
