v^2 = 2gh gives the height h you will climb, and g represents the deceleration due to gravity.
As you might, or might not have noticed, nowhere does the final height that you achieve depend on your mass. Big or small, if you start off with a velocity v and the only thing pulling you back to earth is gravity, then your jump height depends only on the deceleration due to gravity g and your total velocity v. Of course, there is another acceleration that enters into the leap - that provided by your leg muscles at the start of the jump. And this acceleration depends on the mass of the jumper. Using the second law of motion, that force equals mass times acceleration [F=ma] it is clear that for a given force, F, the heavier a person is, the less of an initial velocity he will achieve.
Which means a lower height h that said person will be able to attain.
|I was bitten by a radioactive spider. I can jump as far as a spider can.|
It's not that spiders are such great leapers that they can jump many times their body length. Rather, it's that small insects have tiny muscles (small force), but they only have to lift an equally tiny mass to leap one meter, which just turns out to be many times larger than their sizes. Humans have much bigger muscles than insects, and can output much greater forces, however they also have to lift much heavier masses, so the net effect is that the range/height that they can jump is also about one meter.
TL;DR - F=ma demonstrates how Spiderman's jumping abilities are pure fiction.