For the ball to rebound perpendicularly, the horizontal velocity must reverse direction while the vertical velocity's magnitude is reduced by coefficient of restitution e. Let the angle of incidence be θ. The horizontal velocity component is v cosθ and vertical is v sinθ. After impact, the horizontal velocity becomes -v cosθ (friction absent) and vertical becomes e v sinθ. For perpendicular rebound, the angle with vertical must be 90°, so the horizontal and vertical components must be equal in magnitude: v cosθ = e v sinθ. Solving gives tanθ = 1/e, so θ = tan⁻¹(1/e).

Final answer: ${\tan }^{-1}\left(\frac{1}{e}\right)$