Heating in collisions of solids:possible application to impact craters

Due to the importance of collisions and impacts in early phases of the evolution of the planetary system, it is interesting to estimate the heating of a solid target due to an impact in it . A physically simple calculation of the temperature to which a solid target heats up after the impact of a projectile with mass $m$ and speed $v$ is performed,and possibilities for the application of this result in planetology are pointed out.