There are many problems with the code
v = 82*f[x_]
should be v = 82*f[x]
, similarly for u
.
Take a look at eq02
0 == {{82 Cos[x] (t1 -> (280 Sec[x])/41) - 4.9 (t1 -> (280 Sec[x])/41)^2}}
t1
need to be replaced with the solution for t
t = t1 /. t[[1]]
eq02 = 0 == u*t - (1/2)*g*(t^2)
Solve[eq02, x] // N
(* {{x -> -2.26376}, {x -> -0.877833}, {x -> 0.877833}, {x -> 2.26376}} *)