Question

A 1.0 kg metal head of a geology hammer strikes a solid rock with a velocity of 5.0 m/s. Assuming all the energy is retained by the hammer head, how much will its temperature increase?

Answer 1

1.14degC

Answer 2

1/2 MV^2 is the kinetic energy of the hammer. V is the velocity which is given.
MC delta T is the heat of a compound (m is mass but it cancels, C is the specific heat which you will need to look up AND you need to know what material the hammer is) and delta T is what you solve for. Only one unknown (delta T) IF you know the hammer is made of iron or whatever.

Answer 3

(1/2)MV^2 = M C (delta T)

Solve for the temperaure change: delta T.
C is the specific heat of the metal head. M cancels out and is not needed.
delta T = V^2/(2 C)

C should have units of Joules/(kg C). Use a C value for stainless steel. They should have told you what the geology hammer head is made of.