Question

Find the value of $\theta$ in the diagram given so that the projectile can hit the target

• A. ${\tan }^{-1}\left(\frac{1}{3}\right)$
• B. ${\tan }^{-1}\left(3\right)$
• C. ${30}^o$
• D. ${60}^o$

Answer 1

The correct option is A ${\tan }^{-1}\left(\frac{1}{3}\right)$

$h=10mx=20mv=20m/s$

$t-\frac{20}{20\cos \theta }=\sec \theta$

$v\sin \theta -t-\frac{1}{2}\times 9x{t}^2=10$

$\Rightarrow v\tan \theta -\frac{1}{2}\times 10\times {\sec }^2\theta 10$

$\Rightarrow 20\tan \theta -5-5{\tan }^2\theta =10$

$\Rightarrow {\tan }^2\theta -4\tan \theta +3=0$

$\Rightarrow (\tan \theta -3)(\tan \theta -1)=0$

$\tan \theta =1$ or $3$

$\therefore \theta ={\tan }^{-1}1$ or $ta{n}^{-1}3$