As torque due to gravitational force will be variable, therefore we can use
ΔL=∫0tτdt.
Now, torque of mg at time t =(vxt)mg and horizontal velocity of the projectile will remain constant(vx=vcos45∘=20×21=102).
L0=∫02mg(vxt)dt
=mgvx2t2=(0.1)(10)(102)222
=202
=800kgm2s−1
Therefore, K=800.