Say you have a missile that is launched from the ground at $t = 0$, with an initial velocity of $80.1 ms^{-1}$ at an angle of $57.3$ degrees. At some time it is displaced $200m$ vertically and has a velocity of $50ms^{-1}$ at an angle of $30$ degrees.
Why can I not find the correct time at which the missile reaches $200m$ vertical displacement using $v = u + at$? I attempted to fill it in as: $$t = \frac{50sin30 - 80.1sin57.3}{-9.8}$$
However this got me $4.32s$ when the correct answer is $9.42$, using $s = ut + \frac{1}{2}at^2$. Why does my way not work?