With what speed does the cart recoil if the projectile rises 2.1 m at its maximum height?

In this problem, we assume that the projectile was sent vertically upward. The maximum height reached is calculated through the equation,
                       H = (v²sin²θ)/2g
where H is the maximum height, v is the velocity, θ is the angle (in this case, 90 degrees) and g is the gravitational constant. 
Substituting the known values from the given,
                      2.1 = (v²)(1) / (2 x 9.8) 
                            v = 6.415 m/s
Thus, the initial sped of the projectile is approximately equal to 6.42 m/s. 

Efficiency is an act of doing something

That would be kinetic energy