Question

After one second the velocity of a projectile makes an angle of ${45}^o$ with the horizontal. After another one second it is travelling horizontally. The magnitude of its initial velocity and angle of projection are $(g=10m{s}^{-2})$

• A. $14.62m{s}^{-1},{\tan }^{-1}\left(2\right)$
• B. $22.36ms,{\tan }^{-1}\left(2\right)$
• C. $14.62ms,{60}^o$
• D. $22.36ms{60}^o$

Answer 1

Answer: (B)

$22.36ms,{\tan }^{-1}\left(2\right)$

At $t=1$
$V_y=U_y+gt$
$U\cos \theta =U\sin \theta -g\times 1$
$g=U(\sin \theta -\cos \theta )$
At $t=2$
$Vg=0$
$U_y=gt$
$U\sin \theta =g\times 2$
$g=2g-U\cos \theta$
$U\cos \theta =g$
$\tan \theta =2$
$U=\frac{2g}{\sin \theta }=22.36$