In previous problem, the angular momentum of the projectile about the origin when it just before hits the ground should be.

Options

A. `(- 2 mv_i^3 sin theta sin theta)/(g) hat k`
B. `(m v_i^3 sin theta^2 cos theta)/(2 g) hat k`
C. `(- mv_i^3 sin theta^2 cos theta)/(g) hat k`
D. `(2 mv_i^3 sin theta^2 cos theta)/(g) hat k`.

Answer

A

Explanation

(a) `vec L_2 = R hat i xx m vec v_2`, where
`R = (v_i^2 sin 2 theta)/(g) = (v_i^2 (2 sin theta cos theta))/(g)`
=`-m Rv_i sin theta hat k = (-2 mv_i^3 sin theta sin theta)/(g) hat k`.