Explanation

(a) Using the equation for projectile motion,
$y = x\tan\theta - \frac{gx^{2}}{2u^{2}}\left( 1 + \tan^{2}\theta \right),$ we have
$40 = 30\tan\theta - \frac{g(30)^{2}}{2u}(1 + \tan^{2}\theta)$
or $900\tan^{2}{\theta - 6u^{2}\tan{\theta + \left( 900 + 8u^{2} \right) = 0}}$
For real value of $\theta$
$\left( 6u^{2} \right)^{2} \geq 4 \times 900(900 + 8u^{2})$
or $(u^{4} - 800u^{2}) \geq 90000$
or $\left( u^{2} - 400 \right)^{2} \geq 200000$
or $u^{2} \geq 900$ or $u \geq 30ms^{- 1}$