A particle is projected up an inclined plane of inclination β at an elevation α to the horizontal. Find the ratio between tan α and tan β, if the particle strikes the plane horizontally.
Physics · Kinematics part-2 Projectile Motion · Inclined projectile
JEE Advanced

Question

A particle is projected up an inclined plane of inclination β at an elevation α to the horizontal. Find the ratio between tan α and tan β, if the particle strikes the plane horizontally.

G1 Physics · Accepted Answer

At the instant the projectile strikes the incline horizontally, its vertical velocity is zero, so t = u sinα/g. Then x = u cosα·t and y = u sinα·t - ½gt² = u²sin²α/(2g). Since the point lies on the incline, y = x tanβ. Therefore u²sin²α/(2g) = u²sinαcosα tanβ/g, giving tanα = 2tanβ. Hence tanα/tanβ = 2.