How hard will it be to pull out a 30 year old Dogwood tree from the ground with a 4x4 truck? (if dig around it a few feet deep)?
The more that you can dig out/cut the roots will make it easier to pull down the tree/stump. It can be done with a 4 X 4 truck. I would use a series of large pulleys or block and tackle setup to gain extra leverage in pulling and attach the main pulling ropes as high as possible on the tree to be removed...several+ feet from the ground to gain leverage as well. Attach the pulling ropes and pulleys lower to the ground at attaching points to other trees or anchor objects so that you are pulling with the truck in a straight line versus at an angle which might lift up the back end of the truck. Cut the roots as much as possible on the opposite side of the tree from where you are pulling. Pulley system to pull down tree... https://www.youtube.com/watch?v=vM24klVyxFk
I have taken out a lot of trees. The way to do it is to cut off the top, cut it down to about 15 feet high, remove the branches. Tie a rope to the top. That way when you pull, you get leverage. Too many people make the mistake of cutting the tree right down and losing the advantage of physics. It you pull from the top, you get a lot more leverage. But before you pull, digg around the tree as far as you can around the roots. Use an axe to chop through the roots. DIg out more on the side where you are pulling to so the tree root has some room to move. When you have dug and cut, pull the tree over part way. That will expose more roots. Chop and dig the roots as they appear. Pull more. The most important thing is to put the rope high up so you pull the tree over and down, not up from the roots. The higher the rope, the more leverage you get and the more force you put it.
best practice for homeowner -- rent a stump grinder at your local A to Z [or whatever rental company is nearby]. next best -- dig a lot to expose the roots. Cut roots with chain saw [yes, the dirt is hard on the chain, but a new one is only $20]. then cut stump into pieces. then dig under the pieces and repeat. truck? not much use. the pull you can exert is limited by the strength of the chain you use -- and how are you going to attach the chain around the stump? WORSE -- that chain [or cable] under tension is dangerous -- anyone nearby when it snaps may be whipped by the steel end -- possible severe injury or death resulting [that fast moving end could sever your leg, easily -- ever tow truck driver is endlessly educated about this risk.]
Make sure you video it as you try and pull it out as if it goes wrong it will likely make a great funny video to put up in youtube. I would say you would have a reasonable chance if you can dig down a bit and cut all the major roots.
Depends some on 4x and if you use pulleys and long rope, deadman anchor in ground. Tie rope to top of tree and end to bumper- rear of vehicle will be lifted up and traction lost. Use a ground anchor with pulley- rope at ground level to vehicle will NOT lift wheels, can get fair leverage to tree top then. Angle brace 'lift' at slant to tree so 'lift' up will need a ground anchor for rope to vehicle to keep traction. Old way was dig around, get drill bit about 1 inch to drill hole toward center of stump, then a stick of 25% nitro 'pushing' dynamite inserted with long fuse, mud pack - light and walk(or Run) a ways until 'BOOM' , tree trunk lifts up and fall down various angles. Fill in hole and get chain saw for firewood size chunks. Axe work can take time, chain saw will drop it in a hour safe direction
More force than your truck has TRACTION FOR. If you are digging down a few feet then you will run into many tree roots. Cut them with an axe all around the tree. Leave the rest. They will rot in the ground becoming ground in 10 years as they disintegrate. If you get all the roots on the tree trunk then it is just the weight of the wood and dirt clump that is the roots. . Put dirt in the hole and either plant another tree or pack it and grass seed it. Grass roots do not go deep and another tree, its roots will go around the stuff that is still tree root as it does not dissolve as dirt does. If you are worried about damage to your truck, borrowing your buddies truck...is the solution.
If you cut the roots, you can PUSH it out of the ground without the truck. If you don't the tow trucks used for semis would be stressed to RIP the roots.