Determining the torque and angular momentum of a bullet due to gravity

[texan14]

Homework Statement

A bullet of mass "m" is fired from a cannon located at the origin. The shell moves in the yz plane, where "z" is the vertical coordinate, with an initial velocity of magnitude "v₀" at an angle θ above the y-axis.
A) What is the torque on the shell, about the origin, as a function of time?
B) What is the angular momentum of the shell about the origin as a function of time? (Use the definition of angular momentum to solve)

Homework Equations

Torque = r x F = r*F*sinθ
Angular momentum = r x p = r x m*v = r*p*sinθ

The Attempt at a Solution

My textbook says the answer for A) is -v₀mgtcosθ (in the \vec{i} direction) and -(1/2)v₀mgt²cosθ (\vec{i})

I'm primarily having trouble determining the radius from the origin. I want to say it's v₀cosθ*t, and I want to say the force acting perpendicular to the radius is "mg", but then my answer becomes -v₀mgtcosθsinθ ... Can someone please help?
Also, I'm not sure how to plug momentum into the angular momentum formula to properly find that for part B.

Any help would be extremely appreciated.

 

[curtains forever]

sin(theta) is always 1, because mg acts perpendicular to r.

 

[PeroK]

sin(theta) is always 1, because mg acts perpendicular to r.

Note that this homework is from 9 years ago.