This comment was posted to reddit on May 28, 2015 at 2:30 pm and was deleted within 8 hour(s) and 37 minutes.

The problem is that you can't answer the question with certainty without a few assumptions.

We'd need to assume some things about the maximum force your body/can withstand; the spring constant of the trampoline; and the height of the trampoline.

Your LIMIT is actually decided by your body's ability to accelerate. If you could only withstand 1g (g will be Earth gs here) with your legs then you couldn't jump at all on the Earth, only stand, but you could withstand a jumping acceleration of [1-(1/6)]g on the moon which means you could jump there.

Let's assume you can jump in both cases; meaning your body can withstand more than 1g. Great, now we're stuck with the trampoline issue. What if I have an infinitely tall, infinitely weak trampoline such that the force it exerts on me approaches 0g? You could jump on this trampoline, but it wouldn't work like the system in your head would. It would merely push you at 0N for as far as required to stop your movement and then at the "bottom" you'd still have to push back with your gravitational weight.

Conversely we could have a nearly rigid trampoline which would snap your legs if you landed on it too quickly, much like trying to land while standing after falling from an airplane without a parachute.

Given all this, let's just make it easy on ourselves and assume that the trampoline is designed to travel 2 meters at our maximum acceleration and it has a nice smooth perfect Hook's law response of F = -kx. Great, now we're getting somewhere.

Let's assume the maximum acceleration (a) I can withstand is 10 instantaneous gs. Not devastating as long as it's only for a moment. You'd average out at about 5g, which is fairly typical for a high g roller coaster.

This means I'll be undergoing an average acceleration of 5g over 2 meters.

W = f*d = m*root(2gh) {to find height}

W = 5g*(9.8)*m*2 ~ 100*m

h = about 500 meters on Earth with no resistance

h = about 3000 meters on the moon

enjoy!