have the tires speed balanced if that dont work you may need to replace the due to shifted belts in the tires Your wheels need balancing.
EDIT: Google for " Ford Explorer Aftershake " or similar. It is a very common problem and is a design flaw. Uhaul will not rent equipment behind an Explorer. The "Shake" has to do with the engine and transmission moving back and forth on their mounts at the same frequency that the body of the car is moving from front to back on the rear suspension. More common on 4 door models for some reason. The Ford dealer upgraded the motor mounts and installed a extra shock horizontally in the rear suspension in an attempt correct the problem. The 95 model came standard with the upgrade, but the fix achieved mixed results on the worn suspension of the 91-94 models. There are several technical service bulletins about this problem as the dealerships were working on them under the original warranties many years ago. Read the posts people have made on the internet and see how many parts they have replace only to find out that nothing seemed to correct the problem. I would not recommend working on a FORD EXPLORER without first searching the internet to see what other people have reported about similar problems.
Warped brake rotors........
It is either a front Alignment issue...or the engine needs a lift.
Tires are out of balance
yes!!
The 2003 Ford Explorer has 43.9 in. of front leg room.
The 2007 Ford Explorer has 59.0 in. of front shoulder room.
The 2005 Ford Explorer has 39.9 in. of front head room.
The 2014 Ford Explorer has 40.6 in. of front leg room.
The 2006 Ford Explorer has 59.0 in. of front shoulder room.
The 2001 Ford Explorer has 42.4 in. of front leg room.
The 2013 Ford Explorer has 40.6 in. of front leg room.
The 2010 Ford Explorer has 39.8 in. of front head room.