Amoving hammer hits a nail and drives it into a wall. if the hammer hits the nail with twice the speed, how much deeper will the nail be driven? if the hammer hits with three times the speed?

This is an example of work-energy theorem where it lets a person accumulate the strength of the muscles over the duration of the swing, allowing much bigger forces as the hammer hits the nail.
Moreover, the work done on an object by a net force is equals to the change in kinetic energy of the object, which is expressed as W = KEf - KEi. 
Therefore, if the hammer hits the nail with twice the speed, it corresponds to 4 times the energy and four times the driving distance. If the hammer hits with three times the speed, the driving distance is 9 times as much.  

Jet streams are relatively narrow bands of strong wind in the upper levels of the atmosphere. the winds blow from west to east in jet streams but the flow often shifts to the north and south. jet streams follow the boundaries between hot and cold air. the earth's rotation is responsible for the jet stream as well.