A wheel of radius R is trapped in a mud pit and spinning. As the wheel is spinning, it splashes mud blobs with initial speed u from various points on its circumference. The maximum height from the centre of the wheel, to which a mud blob can reach is

Step-by-step solution

Let a mud blob is detached from the circumference of wheel with initial speed u at angle θ as shown below. Height upto which mud blob can be thrown is h = Maximum height of projectile + Height at which mud blob is thrown h = u 2 sin 2 θ 2 g + R cos θ . . . . i h is maximum when d h d θ = 0 ⇒ d d θ u 2 sin 2 θ 2 g + R cos θ ⇒ u 2 2 g . 2 sin θ cos θ - R sin θ = 0 ⇒ u 2 g · cos θ = R or cos θ = R g u 2 ⇒ sin 2 θ = 1 - R 2 g 2 u 2 Substituting these values in Eq (i), we get λ max = u 2 2 g 1 - R 2 g 2 u 4 + R R g u 2