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Application to free fall

In the case of free fall, we can take our x axis to be in the horizontal direction and the y axis to be in the vertically up. The acceleration of gravity is then tex2html_wrap_inline1934 Instead of writing 9.81, let's just call it g, so tex2html_wrap_inline1936 . We can write down eqs. 5.12 and 5.13 in component form. Again we'll follow the standard notation of using subscripts x and y to denote the components of a vector quantity, so

  equation436

Note that the x component of the velocity is constant, which it should be since there's no acceleration in that direction.

Now for position:

  equation441

and

  equation445

This says that motion of an object in free fall has its x and y components completely decoupled. That is they're independent of each other. If you change tex2html_wrap_inline1938 it doesn't affect the y motion at all. The motion in the x direction is that of an object going at a constant velocity. The motion in the y direction is exactly the same equation as in one dimension for a particle in free fall. By combining these two components, you get the overall motion.





Joshua Deutsch
Mon Jan 6 00:05:26 PST 1997