How to put a variable angle?

Questions
,
1
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I can’t figure out how to find this x? What am I doing wrong?

2

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}} *)
3

There are syntax problems with your code. This gives an answer:

f[x_] = Cos[x];
y[x_] = Cos[x];
v = 82*f[x];
u = 82*y[x];
hd = 560; g = 9.8;
eq01 = hd == v*t1;
t = t1 /. First@Solve[eq01, t1];
eq02 = 0 == u*t - (1/2)*g*(t^2);
Angleanswer = Solve[eq02, x]
4

Thank you very much.

5

Thank you very much.