ClearAll["Global`*"]
u1=Piecewise{0,u≤p},u*Cos[θ]-
2
p
-
2
u
2
Sin[θ]
,u>p∧θ≤ArcSin
p
u
,0,u>p∧θ>ArcSin
p
u
​​u2=Piecewiseu*Cos[θ]+
2
p
-
2
u
2
Sin[θ]
,u≤p,u*Cos[θ]+
2
p
-
2
u
2
Sin[θ]
,u>p∧θ≤ArcSin
p
u
,0,u>p∧θ>ArcSin
p
u

0
u≤p
uCos[θ]-
2
p
-
2
u
2
Sin[θ]
u>p&&θ≤ArcSin
p
u

0
True
uCos[θ]+
2
p
-
2
u
2
Sin[θ]
u≤p||u>p&&θ≤ArcSin
p
u

0
True