Pressure at the walls of a container

[Kaguro]

Homework Statement

Consider a cube ABCDEFGH of volume V containing N molecules each of mass m with
uniform density n =N/V . Suppose this system is equivalent to a system of M non-interacting gases such that molecules of the i th gas are N_i = n_i*V in number, each with an
identical y -component of velocity v_i . What is the pressure P on the surface , ABCD of
area A, perpendicular to the positive y axis?

Relevant Equations

PV=NkT, where N is total number of molecules
Vrms=sqrt(1.5kT)

I wrote energy of each molecule is $\frac{1}{2}mv_{rms}^2 \Rightarrow E/3 = \frac{1}{2}mv_i^2$. So total energy of each type of gas is
$E_i = N_i\frac{3}{2}mv_i^2$ Now, PV=E. So total Pressure = Sum of energies/volume
$P=\frac{\frac{3m}{2}\sum_i N_i v_i^2}{V} =\frac{3m}{2} \sum_i n_i v_i^2$

But answer given is just $m \sum_i n_i v_i^2$
Help.

 

[mjc123]

You are not told anything about the x and z components of the velocity. You cannot assume that they are the same as the y component, or that the pressure is isotropic, so you can't use PV = E.
Incidentally, there is presumably a mistake in the question; at any instant half the molecules have y-velocity v_i, and the other half -v_i.