Question

A body is released from the top of a smooth inclined plane at height h above the ground. Simultaneously another body is pushed up with a velocity u from the bottom. If they meet after time t, an inclination of that inclined plane to the horizontal is

• A. $si{n}^{-1}\left(\frac{t}{hu}\right)$
• B. $co{s}^{-1}\left(\frac{t}{hu}\right)$
• C. $si{n}^{-1}\left(\frac{h}{ut}\right)$
• D. $co{s}^{-1}\left(\frac{hu}{t}\right)$

Answer 1

The correct option is C $si{n}^{-1}\left(\frac{h}{ut}\right)$

Acceleration on the inclined plane is $\pm g\sin \theta$
$S_1=\frac{1}{2}\left(g\sin \theta \right)t^2$ down the inclined plane
$S_2=ut-\frac{1}{2}g\sin \theta t^2$ up along the inclined plane
$S=S_1+S_2=ut$
$\frac{h}{\sin \theta }=ut$
$\theta ={\sin }^{-1}\left(\frac{h}{ut}\right)$