a jet of water of cross sectional area A and velocity v impinges normally on a stationary flat plate. the mass per unitvolume of water is p. by dimensional analysis determine an expression for the force F exerted by the jet against the plate.

good question...
i am giving u the actual formula and u can also write it using dimensions...
F= ma
= pVa {where p is density, v volume and a acceleration)
=pV((u-v)/t) { by defination a=(v-u)/t  where u is initial velocity, and v is final velocity in time t}

now, u=v(by question) and v=0 (as the water does not rebounds)
=pV(v-0)/t
=pVv/t
now voloume can be expressed as V = A*x where A is the cross sectional area and x is the distance travelled by the jet

so, F= pAxv/t
or F= pAv(x/t)
Now distance travelled per unit time is velocity itself i.e., x/t=v
so, F=pAvv = pAv^​2

if you want the dimensional analysis only then
[F]= [MLT^-2]
=[ML^-3][L²][L²T^-2]
=[ML^-3][L²][LT^-1]²
Now by defination and putting the appropriate values as per the question
we get:
F=pA(v)²
=pAv² ans...