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Unformatted text preview: peed,
i.e. ver tical acceleration, which in our case is g for gravity. height y(t) = u . s i n θ . t -- 1 g t 2
-2 (0,0) T T/ 2 t y ’(t) = u . s i n θ -- g t
-- g = gravity y ”(t) = -- g (the minus sign indicates the downward direction of gravity) d2
= dt2 (u . s i n θ . t -- -- g t ) = -- g
As with any calculation there are two par ts: the operation p ar t and the
units of measur e p ar t. Here the height is measured in [meters] and time t
is measured in [secs]:
Vertical acceleration : y ”(t) = [meters]
y = vertical position or height [meter s]
y ’ = s peed [meter s / sec]
y ” = a cceleration [meter s / sec 2 ]
81 Deriv tiv
Deri v a ti v e of the inv er se function
Let y = x2 . Then the inver se function is : x = y ½. We may now differentiate the
inver se function x with respect to y to get dx/dy = 1/ 2y ½. Alternatively, we know
that dy/dx = 2x. Hence:
Now we may substitute x = y ½ to get the derivative of the inver se function x with
respect to y : dx/ dy = 1/ 2y ½ . So the derivative of the inver se function x is:
entiation parametric or
Dif f er entia tion in par ametric ffor m
We have now learned to find the INSTANTANEOUS RATE OF CHANGE of a
function. The reader should ask the question: what about the INSTANTANEOUS
RATE OF CHANGE of one function with respect to another function of the same
A plane flying horizondally at a speed of 600 kms / hour descends at the rate of
1200 feet / minute. What is the glide ratio ?
horizontal speed u’(t) = 600 kms / hour ≅ 500 feet / sec
downward speed v’(t) = 1200 feet / minute = 20 feet / sec
speed glide ratio = horizontal speed u’(t)
downward speed v’(t)
speed 500 feet / sec
20 feet / sec That is to say, for every 25 feet forward the plane looses height (descends) by 1 foot.
Notice the absence of the time...
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This note was uploaded on 11/29/2012 for the course PHYSICS 105 taught by Professor Tamerdoğan during the Fall '09 term at Middle East Technical University.
- Fall '09