Question

Find the value of $\theta$ in the diagram so that the projectile can hit the target.
$(\text{Take}g=10m/s^2)$

• A. ${45}^{\circ }$
• B. ${\tan }^{-1}\left(5\right)$
• C. ${60}^{\circ }$
• D. ${\tan }^{-1}\left(3\right)$

Answer 1

Answer: (A), (D)

The correct options are
A ${45}^{\circ }$
D ${\tan }^{-1}\left(3\right)$

Equation of trajectory is given as;
$y=x\tan \theta -\frac{g{x}^2}{2u^2{\cos }^2\theta }10=20\times \tan \theta -\frac{10\times {20}^2}{2\times {20}^2}\times \left({\sec }^2\theta \right)2=4\times \tan \theta -(1+{\tan }^2\theta ){\tan }^2\theta -4\tan \theta +3=0\text{On solving the above quadratic equation}\text{we get the value of}\tan \theta \text{as}\tan \theta =3,1\theta ={45}^{\circ }\text{or}{\tan }^{-1}\left(3\right)$