A particle of mass m is projected from the origin with an initial speed u at an angle with the horizontal. The magnitude of the angular momentum of the particle about the point of its maximum height, evaluated at the exact instant the particle strikes the horizontal ground, is

Step-by-step solution

Let the point of projection be the origin (0,0) . The coordinates of the highest point P are ( R 2 , H ) = ( u^2 2 2g , u^2 ^2 2g ) . The coordinates of the landing point Q are (R, 0) = ( u^2 2 g , 0 ) . The position vector of the landing point relative to the highest point is: r ' = r _Q - r _P = ( R - R 2 ) i + (0 - H) j = R 2 i - H j . At the instant of landing, the velocity vector of the particle is: v = u i - u j . The angular momentum of the particle about the highest point is given by L = m ( r ' v ) . r ' v