Note: supercat's answer was the closest to what I was intending. I've started a second question to ask a better way to phrase this puzzle that will allow more people to recognize the solution without the list of caveats I had to create here.
I'm making edits as holes are pointed out to narrow down the question and avoid misdirection. If this negates an answer you gave, I am sorry. I'm trying to make this a workable puzzle. Ideally, it could be told verbally without much loss.
I intend to post a separate question asking how to improve this one since it is obviously too open right now. There's a big difference between the restrictions required for posting here and the restriction required when asking "normal" people in person.
Robot Long and Robot High are tootling along via their preferred method of locomotion when they come to a gorge. They want to get to the other side and they must jump to do so.
Here's the problem, though: At it's narrowest point, the gap is just skinny enough that Robot Long can make the jump. Robot High can jump a little higher than Robot Long but it can't jump as far. If Robot High tried to make the jump, it would plummet to its doom. They are extremely accurate and precise jumpers, able to always jump the same distance at the same speed. They have only two speeds: Stopped and Moving. On each side of the gorge, there's only enough space for one robot to jump or land at a time. (The skinny point is a narrow strip jutting out from the cliff face.)
How do they get across?
Because this puzzle is not optimized, I must make several clarifications. Please help me improve this puzzle so I don't have to list off all these restrictions:
- There are no other materials available.
- Not even grass grows here and the robots are not engineered for digging.
- Climbing down and back up are not an option as they are not engineered for climbing.
- There are no bridges or other resources available.
- Going around the gorge is not possible at it encircles the entire planet, this being the narrowest point.
- Jumping is their only option.
- They can not stand atop one another as that would weaken their jumping ability such that they would both plummet to their doom.
- There are no means by which they can combine their jumping power such as holding hands (grabbers?) or tying together.
- The distances described for their jump limits are the furthest they can jump under the best circumstances.
- The bottom is far enough that they would be destroyed should they fall.
- Air friction can be neglected.
- Assume the ground speed for both robots is fixed. (The planet is large enough and they're not jumping high enough that you can assume air speed is the same as ground speed.)
Here is an incredibly precise and detailed diagram of their position and jumping abilities that I have rendered in amazing 3D if you move your head forward and backward very quickly: (not to scale)