Question

A projectile of mass m fired with velocity u making angle θ with the horizontal, its angular momentum about the point of projection when it hits the ground is given by 

(a) (2mu sin²θ cosθ) / g 

(b) -(2mu³ sin²θ cosθ) / g 

(c) (mu sin²θ cosθ) / g 

(d) (mu³ sin²θ cosθ) / g

Answer 1

Answer is (b) -(2mu³ sin²θ cosθ) / g

L = vector(r x p) = vector(R x P) where R = range = (u² sin 2θ)/g. 

the angle between vector(R & p) is = θ. Also p = mu.

Hence L = [(u² sin2θ) / g] x mu sin (-θ) = -(2mu³ sin² θ cos θ] / g .