Question

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

• A. tanβ
• B. 2 tanβ
• C. 3 tanβ
• D. 1/2 tanβ

Answer 1

Answer: (D)

1/2 tanβ

Answer 2

As the particle strikes the plane horizontally, its velocity is parallel to horizontal axis so its vertical velocity is given by

0 = u sin β - gt(v = u + at)

or u sin β = g $\left\lbrack \frac{2u\sin(\beta - \alpha)}{g\cos\alpha} \right\rbrack$

( t is time of flight)

or sin β cos α = 2[sin β cos α - cos β sin α]

or 2cos β sin α = sin β cos α

or 2$\frac{\sin\alpha}{\cos\alpha} = \frac{\sin\beta}{\cos\beta}$

or 2 tan α = tan β or tan α = 1/2 tan β