Before thinking about how grasshoppers solve the power problem of
muscles, let's think about how humans solve the same problem.
Exactly the same difficulty faces a human who wants to throw
something as faces a grasshopper that wants to throw itself (after
all, that's what jumping is - throwing yourself with your legs). A
good throw needs a rapid and forceful arm movement, but as we have
just said, muscles can produce high force or high speed, but not both.
Humans have solved this problem by using tools, such as the catapult,
or bow-and-arrow.
What is going on here?
The archer draws back the bow slowly. This means that her arm muscles can contract with the maximum force of which they are capable.
The energy of the muscle contraction is stored in the bending of the bow.
The archer lets go of the bow string, and ...
The bow springs back, transferring the energy from the bow to the arrow (potential → kinetic energy).
The KEY POINT is that athough the bow is bent very slowly, it springs
back very quickly. It can do this because it does not suffer from the same force/speed trade-off that muscle does - it can move with both high force and high speed.
The arrow zooms off towards the target, and the rest is history.
Thus in summary, the archer uses her arm muscles to store energy in
the bow slowly, and the bow then transfers this energy to the
arrow quickly. In physics terms, the bow is acting as a power
amplifier.
So what has all this got to do with grasshoppers? The answer is that
grasshoppers developed their very own catapults about 100 million
years before humans ever thought of them. This catapult is built into
the back legs of every grasshopper.