.177 7.8 grn Gamo Redfire vs back of Gopher head/skull

Hi all, today I caught another busy digging up the yard again. I grabbed my Gamo Varmint and loaded a Gamo Redfire 7.8 grn pellet and wacked it in the back of it's head from around 15 ft. with a Gamo Varmint .177 rated at (printed on the barrel) 1250 fps.
From that range I don't think I could have missed. Problem is, I took a shovel to dig it up and found nothing. The ground is super hardpacked and rocky so I didn't get very far yet.
My question is, is that combination enough to penetrate the back of a gophers skull?
 
Hi all, today I caught another busy digging up the yard again. I grabbed my Gamo Varmint and loaded a Gamo Redfire 7.8 grn pellet and wacked it in the back of it's head from around 15 ft. with a Gamo Varmint .177 rated at (printed on the barrel) 1250 fps.
From that range I don't think I could have missed. Problem is, I took a shovel to dig it up and found nothing. The ground is super hardpacked and rocky so I didn't get very far yet.
My question is, is that combination enough to penetrate the back of a gophers skull?
Yes it will work.

If it doesn't make a sonic crack it's not going that 1250 fast. But let's just use 850 fps as your velocity. With your 7.8 grain pellet hypothetically traveiling at 850 fps you have 12.51 foot pounds of muzzle energy. So you're already better off that most brits or Germans. My friends and I have found it takes as little as 1.5 foot pounds for some small rodents at closer ranges like yours. Or 300 fps with your pellet.

Have fun.