Mass of Mars: 6.4*10^23 kg
Mass of Earth: 6.0*10^23
Assume that a Mars-sized proto-planet collides with the Earth. Velocity on impact is 4 km/s.
Assume that all kinetic energy of the proto-planet is converted into heat and that the heat produced raises the temperature of the combined Earth-proto-planet system.
Heat capacity of rock: 0.8 kilojoules per kg per degree Kelvin
One joule=one kg m^2s^-2
By how many degrees would the temperature of the Earth proto-planet system be if all the kinetic energy were converted into heat