Question

Two second after projection, a projectile makes an angle of ${30}^o$ with the horizontal. After one more second it is moving horizontally.Find the angle of projection.

• A. $0^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is C ${60}^o$

At any point on the trajectory of a projectile, we have:
$\tan \alpha =\frac{v\sin \alpha }{vcos\alpha }=\frac{u\sin \theta -gt}{u\cos \theta }$

At $t=2s$,

$\frac{u\sin \theta -2g}{u\cos \theta }=\tan {30}^0$ ........................................ (1)

Also, at $t=3s$,
$u\sin \theta -3g=0$

$\Rightarrow \frac{u\sin \theta }{g}=3$ ........................................................ (2)

From (1) and (2), we get:

$\frac{3g-2g}{u\cos \theta }=\tan {30}^0\Rightarrow u\cos \theta =\sqrt{3}g$

and $u\sin \theta =3g$

$\Rightarrow \tan \theta =\sqrt{3}\Rightarrow \theta ={60}^0$