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This is a "recipe" for solving word problems. Slightly
rewritten, it can be a guide to solving ANY problem. You've
been following this procedure for years, probably
unconsciously. While this is not "the only way," if you
stick to this procedure, solving problems should become
steadily easier.
- Write down what is given in the problem. Yes,
yes, I know it's right there, but writing it all down
on your own sheet of paper helps you focus more.
- Determine and write down what you are expected
to find. Sometimes this can be the hardest part...
- Make a sketch of the problem, labeling all
quantities. Sometimes, this may not be necessary.
- Find a way to relate what you've been given to
what you need to find. Often this involves a formula
or equation, which must occasionally be rearranged to
suit our needs.
- Make sure the units of the data are compatible
with the formula and with each other. This is a VITAL
step and MUST NOT be omitted!
- Perform the calculations and get the answer.
Always check your answer to make sure it makes
sense!
Here's an example of this procedure:
The average distance between the Earth and the
Moon is 384,000 km. The Moon takes 27.3 days to orbit the
Earth once. What is the Moon's orbital velocity, in
km/sec? Assume the Moon's orbit is circular.
- Our information is all in the problem: Distance
between Earth and Moon = 384,000 kilometers and Travel
time = 27.3 days.
- We want to find v, the orbital velocity, so v =
?
- No sketch needed, but we should bear in mind that
the Moon travels in a near-circle around the
Earth.
- The formula for velocity is v = D / T, where D is
the distance the object travels, and T is the amount
of time it takes to travel. Now the distance the Moon
travels in its orbit is not the radius of the orbit;
it's the distance around the orbit, called the
circumference. The formula for circumference is C =
2(pi)R.
- We're asked for the velocity in km/sec, and the
distance is in kilometers, so we're halfway there. We
must convert the orbital period from days into
seconds:
T = 27.3 days X ( 24 hrs / day ) X ( 60 min /
hr ) X ( 60 sec / min )
T= 2,358,720 seconds
- Plug in the values into the formula v = D/T =
2(pi)R/T:
-
V = 2 (pi) (384,000) / (2,358,720) = 2,412,743 km
/ 2,358,720 sec
V = 1.023 km/sec
So the velocity of the moon in its orbit
is a little over 1 kilometer per second. Pretty
fast!
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Updated
8/25/99
By James
E. Heath