Question

A 3.00-g copper penny at 25.0°C drops from a height of50.0 m to the ground. (

Answer 1

The potential energy, E, of the penny is given by E=mgh.  The energy, Q, required to raise the temperature of an object by an amount ΔT is given by Q=mcΔT.  We can equate these two to get the result but we must use proper units and include the 60%:
(0.6)mgh=mcΔT
We see we can divide out the mass from each side
0.6gh=cΔT,   then 0.6gh/c=ΔT
(0.6)9.81(m/s²)50m/385(J/kg°C) = 0.7644°C
since this is the change in temperature and it started at 25°C we get
T=25.7644°C
As you can see the result does not depend on mass.  The more massive the copper object the more potential energy it will have to contribute to the heat energy, but the more stuff there will be to heat up, and the effect is that the mass cancels.