Our 89 Jeep cherokee took a shot in the passenger front tire in an accident. Now at certain speeds the front end begins to shake drastically.

First thing to check is air pressure,
Second is to have that wheel put on a spin balance machine to see if the tire's steel bend shifted,or the wheel got bent,or a weight came off.
If all those check out,Then check the steering for any loose parts,
The last is check the front alignment.

Did your Jeep fight back? Someone takes a shot at me and I'm going shake a bit to. But probably not for the same reason.

Issues that could cause shaking:

• Out of balance tire.
• Deformed tire.
• Damaged or broken belt inside the tire.
• Bent rim.
• Out of alignment.

Your problem could be anyone or any combination of the above items.

You need to take the Jeep in and have the tire and rim checked for any sign of damage or out of balance.
If you don't take care of this bad things can happen.
The primary one is that even though you only feel the shaking a a certain speed, it is shaking all the time. After a certain point that shaking can turn into a high frequency vibration. This vibration is sometimes hard to feel but it will have a huge impact on the Jeep over time. One effect is the lug nuts can become loose and eventually cause the tire to change lanes without telling you or the rest of the Jeep in advance.

Also there is a fifty percent chance that I painted part of that Jeep and I would really be upset if took another shot. So please take care of it as well as yourself and get the tires checked.
Hope this helps and good luck.

P.S.
Tell Jeep I said hello and stay out of trouble.
It's rough being the parent of over 20.000 Jeeps.

Shaking like that is generally called "death wobble" and is generally attributed to a loose component in the front end...usually ball joints, track bar (or track bar mount) or cracked frame at the steering box attachment points.
In your case, since impact was involved, I'd also make certain that nothing has bent and has changed the front wheel caster angle as a negative angle can also cause wobble (like a bad wheel on a shopping cart) This needs to be checked by an alignment specialist as many parts have a factory bend and differentiating between something that happened from an impact and something that is supposed to be that way is often difficult. Slight bends can be compensated for during an alignment but many times the part must be replaced. After any impact it is wise to have everything checked over. Your problem could be as simple as a broken belt inside a tire but usually that would give you a slight wobble even when going slow.