I had a lot of trouble with this task, so here's a little guide in case you are, too.

Okay, so the big red button is a pad that you have to put pressure on, right? Well, turns out, size really doesn't matter in this case, momentum does. You have to drop something from up high, like the ceiling. I personally like using myself because I can control my fall to make sure I actually land on the button.

Then, all you have to do is press the smaller red button with one of your webs and, voila! You just launched your rocket.

in my room, launching my rocket. and, by "rocket", let's just say... my plastic toy rocket ship.