Question

Please can someone explain me ho to rearrange the following formula to obtain t

y =(V*sin(d))*t - 0.5*g*t^2

I trying to solve a problem by time and I can't see how to get this.

here is the values in my work
y = -35
d = 25
g = 9.8
v = 80

my book shows the final answer t = 7.814

Answer 1

\[y = V \sin(d)t - \frac{1}{2} g t^{2}\]
\[g t^{2} -2 V \sin(d) t + 2y =0\]
\[t = \frac{2V \sin(d) \pm \sqrt{4V^{2}\sin^{2}d - 4 (g)(2y)}}{2g}\]

i suspect you have an easier way to do this

eg use \[v^2 = u^2 + 2 a x \]
as an intermediate step and then use \[v = u + at\]