Question

A particle is projected up an inclined plane of inclination $\alpha$ to the horizontal. If the particle strikes the plane horizontally then $\tan \alpha =$

• A. $\tan \beta$
• B. $2\tan \beta$
• C. $3\tan \beta$
• D. $\frac{1}{2}\tan \beta$

Answer 1

Answer: (D)

$\frac{1}{2}\tan \beta$

For motion on inclined plane time of flight $T=\frac{2u\sin (\beta -\alpha )}{g\cos \alpha }$
As the particle strikes the plane horizontally, its velocity is parallel to horizontal axis, so vertical velocity component is, $0=u\sin \beta -gT$

$u\sin \beta =g\frac{2u\sin (\beta -\alpha )}{g\cos \alpha }or\sin \beta \cos \alpha =2\cos \beta \sin \alpha \Rightarrow \tan \alpha =\frac{1}{2}\tan \beta$