Even though the jumping solution sounds right, it isn’t. The reason is that to jump high, you need to transfer as much energy as possible from your legs into the ground, but this gets harder to do as you get smaller.
If you were shrunk down to the size of a penny, you’d only have a fraction of a second between starting the jump and your feet leaving the floor, so your muscles would need to contract really fast to transfer that energy. The problem is that the faster your muscles contract, the less force they are able to produce, an effect called the force-velocity relationship.
So you might need to look for a better answer to this question, which isn’t that complicated either.
This might be the correct answer.
Professor Sutton believes that using a catapult system to get out would be the right answer to this tricky question, “If I were shrunk down and put in a blender, I’d use a small rubber band to fling myself out. The catapult system would work great at that size because your strength-to-mass ratio is very beneficial even if your jumping mechanisms don’t work so well.”
Professor Jim Usherwood, an expert on the mechanics of motion from the Royal Veterinary College, mentioned another solution, “If you want to make something go fast, you need to give it a lot of energy. If you have really short arms, it has left your hand before you have time to give it that energy, as muscle power is limited – unless you can wind up a spring.”
“When you’re shooting a bow, you don’t need to move your body fast in order to accelerate the arrow to a great speed. Instead, you can move slowly and use your strength to store a massive amount of energy in a spring and release it very quickly.”
So here it is: if you could wind up a spring over a suitable time – about 0.1 seconds – and then release it, you could ping yourself out of the blender.