# Solve 0.342costheta+hcos^2theta=16(D)^2/V_0^2, if V_0=60, D=80 and h=2?

Apr 9, 2017

There is no solution.

#### Explanation:

As ${V}_{0} = 60$, $D = 80$ and $h = 2$

$0.342 \cos \theta + h {\cos}^{2} \theta = 16 {D}^{2} / {V}_{0}^{2}$ becomes

$0.342 \cos \theta + 2 {\cos}^{2} \theta = 16 \times \frac{6400}{3600} = \frac{256}{9}$

Hence this becomes

$18 {\cos}^{2} \theta + 3.078 \cos \theta - 256 = 0$

$\cos \theta = \frac{- 3.078 \pm \sqrt{{3.078}^{2} + 4 \times 18 \times 256}}{36}$

= $\frac{- 3.078 \pm \sqrt{9.4741 + 18432}}{36}$

= $\frac{- 3.078 \pm 135.8}{36}$

= $3.6868$ or $- 3.858$

As domain of $\cos \theta$ is $\left\{- 1 , 1\right\}$ and roots are beyond this range

There is no solution.