A particle is projected perpendicularly to an inclined plane as shown in the figure. If the initial velocity of the particle is u, calculate how far from the point of projection does it hit the plane again if the distance is measured along the plane?

Question

G1 Physics · Accepted Answer

Take x along the incline and y normal to it. The particle is launched normally, so uₓ = 0 and uᵧ = u. Gravity components are aₓ = g sinθ down the incline and aᵧ = -g cosθ. It returns to the plane when y = ut - ½gcosθ·t² = 0, giving T = 2u/(gcosθ). Hence range along the plane x = ½g sinθ·T² = [2u²/g]·sinθ/cos²θ = (2u²/g)tanθ secθ. Therefore option D.