A particle is projected up an inclines plane. Plane is inclined at an angle `theta` with horizontal and particle is projected at an angle `alpha` with horizontal. If particle strikes the plane horizontally prove that `tan alpha=2 tan theta`

Answer

2

Explanation

[2]: We can understand that it is equivalent to half of the path of ground -to-ground projectile .

`tan beta =(2H)/(R)`
`tan beta =((2(u^(2)sin^(2)alpha)/(2g))/(u^(2)sin2alpha))/(g)=(sin^(2)alpha)/(sin2alpha)=(sin^(2)alpha)/(2sin alpha cos alpha)=(1)/(2)tan alpha`
`rArr (tan alpha)/(tan beta)=2`
Hence, answer is 2.