Key idea - total angular momentum of the system is conserved. Before the collision: angular momentum of earth is given by L_{E}=I*w*_{E}, here w_{E }is the angular velocity of Earth and I is its moment of innertia which is given by I=2/5M_{E}*R*^{2}. R is the radius of Earth and M_{E} is its mass. Angular momentum of the asteroid is L_{A}=mv*d. Here m is asteroid's mass, v its velocity and d the perpendicular distance of its trajectory from the centre of the Earth given by d=sin(45°)**R (see the whiteboard).*

After the collision (inelastic) the asteroid is stuck to the surface and the whole system rotates at different angular velocity w_{F}. Total angular momentum is therefore given by L_{F}=Iw_{F} + mR^{2}*w*_{F}.

By equating the two angular momenta we obtain an equation from which we can express v - the asteroid's velocity. By neglecting the asteroids mass compared to the mass of the Earth (factor of 10^{8}) we obtain an approximate expression v=(I(w_{F}-w_{E}))/(m*sin(45°)*R) = 15.9*10^8 i.e. faster than the speed of light!! This means that our classical approximations break down and we need to treat the whole problem relativistically which is well beyond the scope of A level Physics.