A heavy particles is projected from a point at the foot of a fixed plane, inclined at an angle `45^(@)` to the horizontal, in the vertical plane containging the line of greatest slope through the point. If `phi(gt45^(@))` is the inclination to the horizontal of the initial direction of projection,for what value of `tan phi` will the particle strike the plane horizontal.

Answer

B

Explanation

Let the particle be projected from `O` with velocity `u` and strike the plane at a point `P` after time `t`.
Let `ON=PN=h`, then `OP=hsqrt2`.
If the particle strikes the plane horizontally, then its vertical component of velocity at `P` at zero. Along horizontal direction
`h=(u cos phi)(t) ....(1)`
Along vertical direction, `0=u sin phi-"gt"`
or `u sin phi ="gt"`...(2)
and `h=u sin phi t-1/2"gt"^(2)` ---(3)
Using eqns.(1) and (2) in (3)
`(u cos phi )(t)=(u cos phi )(t)-1/2(u cos phi )(t) tan phi=2`