How Does Projectile Angle Affect Flight Time on an Inclined Plane?

[cscott]

A projectile is fired up an inclined plane with an initial speed vi and at an angle beta with respect to the incline, which, in
turn, rises at an angle alpha with respect to the horizontal.

(b) Determine the time of flight, tflight from when the projectile is launched to when it strikes the inclined plane.
Express your answer in terms of alpha, beta, vi and g.

(c) Determine a second expression for the time of flight based on the condition that the projectile strikes the inclined
plane with a final velocity that is perpendicular to the plane. Again, express your answer in terms of alpha, beta, vi and
g.

(d) Using your results from parts (b) and (c), find the angle beta and the values for the initial speed, vi , for which the
final velocity is perpendicular to the inclined plane. If your answer surprises you a clever use of dimensional
analysis may provide some insight.

I have my two expressions for time for (b) and (c) but I'm not sure how to use them to get the angles or values for initial velocity.

(b)$$t = \frac{2v_i\sin \beta}{g \cos \alpha}$$
(c)$$t = \frac{v_i cos \beta}{g \sin \alpha}$$

 

[semc]

hmm...i have yet to try the question but looks interesting...IF we were to assume angle alpha-beta to be zero which means the projectile is on a flat ground,does tt mean tt when the projectile hits the ground,Vy=0?