Calculate the constant acceleration a in g’s which the catapult of an aircraft carrier must provide to produce a launch velocity of 188 mi/hr in a distance of 299 ft. assume that the carrier is at anchor.

The solution to the problem is as follows:

First, I'd convert 188 mi/hr to ft/s. You should end up with about ~275.7 ft/s.
 
So now write down all the values you know:

Vfinal = 275.7 ft/s

Vinitial = 0 ft/s

distance = 299ft

Now just plug in Vf, Vi and d to solve

Vf^2 = Vi^2 + 2 a d 

BTW: That will give you the acceleration in ft/s^2. You can convert that to "g"s by dividing it by 32 since 1 g is 32 ft/s^2.