Aprojectile is fired from the origin of the coordinate system with an initial velocity v0 in a direction making an angle α with the horizontal. calculate the time required for the projectile to cross a line passing through the origin and making an angle β < α with the horizontal.

Explanation:

Given

launching inclination is

suppose u is the initial velocity

vertical velocity

horizontal velocity

Vertical distance traveled by Projectile is

Now equation of line passing through origin

Equating two equation we get

putting

snell's law

refractve index = sin incidence / sin refraction