Frankly, i think one of those hand-held water rockets in the hands of a
3-year old is an accident waiting to happen. 3-y olds just don't have the
coordination or one-handed strength to point such a rocket in an appropriate
direction at the same time they are pulling (usually stiff) trigger
mechanism.
The stomp rockets are better, but a 3-y old's mass doesn't make for much in
the way of stomping power, and the kids are a bit prone to falling over in
their enthusiastic attempts to "jump harder"...
The pump and launch stand based air and water rockets (like the estes air
hog rocket, or the nerf rocket launcher) actually work pretty well, with a
bit of supervision. They tend to contain devices designed to make sure they
are launched only when pointing upward, which a 3-y won't understand very
well, leading to some frustration, but it makes them relatively safe unless
they manage to hang their bodies directly over the launcher (which they
WILL, given a chance. Even "safe" toys need a bit of supervision.) Kids
can probably pump them up enough to get SOME flight, and will be impressed
at how strong dad or big brother is, and how high the rocket goes with
THEM pumping it up... :-)
A 3-y old is well capable of "helping" dad build an estes-style or high
power sized rocket (they can at least pour paint on it...), and appreciating
a real model rocket launch, even with its attendent safety rules, as long as
it doesn't drag out for too long. Bigger rockets are better, but actual HPR
motors are likely to be too noisy for most of them... fly with a club, and
there's lots of spectating to do in between your own launches.
Finally, there are interesting things you can do with staws, tape for nose
and fins, and perhaps an ear syringe. And these "rocket balloons" work
pretty well too:
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(however, don't forget that balloons are currently villified as one of
the most dangerous toys commonly given to small children. Several kids
a year manage to suffocate on balloons or balloon pieces that they get
stuck in their respiratory system, and the balloon pieces tend to be
soft enough that they're difficult to get out via standard first aid
procedures. While many small toys are restricted to children over three
years of age, I've seen suggestions that balloons are only for kids over
8. I think it's a bit ridiculous. Using a pump for inflation rather
than the mouth probably helps a lot...)
BillW