A horizontal smooth square platform $\mathrm{ABCD}$ is moving towards the right with a uniform speed $v$. At what angle $\theta$ must a particle slide from $\mathrm{A}$, on the platform, with speed $u$ so that it strikes the point $\mathrm{B}$? (Assume $u$ to be uniform and $u > v$)

• A

  ${\text{sin}}^{-1}\left(\frac{u}{v}\right)$
• Correct answer
  B

  ${\text{cos}}^{-1}\left(\frac{v}{u}\right)$
• C

  ${\text{cos}}^{-1}\left(\frac{u}{v}\right)$
• D

  ${\text{sin}}^{-1}\left(\frac{v}{u}\right)$

Solution

$\Rightarrow \text{u}\text{cos}\theta \text{t}=\text{v}\text{t}$

$\Rightarrow \text{u}\text{cos}\theta =\text{v}$

$\text{cos}\theta =\frac{\text{v}}{\text{u}}$

$\theta ={\text{cos}}^{-1}\left(\frac{\text{v}}{\text{u}}\right)$

Hence, the correct answer is option: 'B'.