Q:

Find the minimum value of velocity

Find the minimum value of the initial velocity $u$ of the particle such that the particle crosses the wheel of radius $R$.

Details and assumptions
$R=2m$
$g=9.8m/s^2$
Neglect air resistance.
All surfaces are frictionless.
The value of $\theta$ (angle the projectile makes either with vertical or horizontal), range and $u$ is not known.
Consider the motion in 2-D space only.

I tried setting the maximum height equal to $2R$ and then finding the corresponding minimum value of $u$, but my answer was incorrect.
  Then I tried to set the latus rectum of the parabola (equation of trajectory) equal to $2R$ but that too didn't work.
  Can anybody suggest a way to do this question?
  Thanks in advance!  

A:

The value of initial velocity will be different for different angles θ with the horizontal.. So I got this result.
$$
u=(gR/(sinθcosθ-cos^{2}θ))^{1/2} 
$$
or
$$
u=(2gR/(sin2θ-2cos^{2}θ))^{1/2}
$$
or
$$
u=(39.2/(sin2θ-2cos^{2}θ))^{1/2}
$$
This is my attempt for the solution(i have attached image):
From A to B displacement is FB
From C to B displacement is EB

and θ should be greater than π/4 so that the particle will touch at two points
is the answer correct?

