The problem is a physics one, specifically dealing with a perfectly inelastic collision in one dimension. By applying the conservation of momentum, we can find out the final velocity and its direction. The calculations involve subtracting the product of the second asteroid's mass and velocity from the product of the first asteroid's mass and velocity, then dividing by the sum of their masses.
The problem at hand involves a perfectly inelastic collision between two asteroids where they stick together after the collision. Using the conservation of momentum principle, we can calculate the magnitude and direction of the velocity of the new asteroid after the collision. The equation for conservation of momentum in one dimension for two masses A and B before and after collision is given by:
mA × vA + mB × (-vB) = (mA + mB) × v'
In this formula, v' is the final velocity of the combined mass after the collision, and the negative sign for vB indicates that asteroid B is moving in the opposite direction to asteroid A. After carrying out the necessary calculations using the provided masses and velocities, we can arrive at the final velocity and its direction.