Explain how using dimensional analysis could have prevented this crash

Dimensional analysis is a convenient technique to determine if the solution you're following would lead you to the answer that you're looking for. It is the manipulation of units. Like units are cancelled whenever they appear on the numerator and the denominator side. For example, if the speed is 5 m/s and the time is 2 s, the distance would be:

(m/s)*(s) = m

So, you would know that the solution would be 5*2 because it yields the unit for distance. 

Hence, dimensional analysis could prevent crash by calculating the right velocities or distances of the two vessels to prevent collision.