theodore0307
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I need help with the following question, 
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Please show working out
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Question on Application of Calculus to the Physical World (1 Viewer)
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rumbleroar
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a. t = 0
b. find h', let it equal to 0 (prove it is max as well) for max dist
c. acceleration, iirc is h", so sub t=0 and tmax into h" for the acceleration at these times
b. find h', let it equal to 0 (prove it is max as well) for max dist
c. acceleration, iirc is h", so sub t=0 and tmax into h" for the acceleration at these times
Alternatively:
(b) Realise that the max/min values of the sine function are +/- 1.
These values will give the most +ve and most -ve displacements of +/- 3.
sin2t = +/- 1 when 2t=pi/2, 3pi/2, 5pi/2, ...
ie. t = pi/4, 3pi/4, 5pi/4, ...
(c) If you differentiate twice you get -12sin2t, and remembering that h=3sin2t, you get acc=-4x
Since the displacement at these points is x= +/- 3, then the acceleration is -/+ 12
(b) Realise that the max/min values of the sine function are +/- 1.
These values will give the most +ve and most -ve displacements of +/- 3.
sin2t = +/- 1 when 2t=pi/2, 3pi/2, 5pi/2, ...
ie. t = pi/4, 3pi/4, 5pi/4, ...
(c) If you differentiate twice you get -12sin2t, and remembering that h=3sin2t, you get acc=-4x
Since the displacement at these points is x= +/- 3, then the acceleration is -/+ 12