MATH102 December 2011
• Q1 (a) i • Q1 (a) ii • Q1 (b) i • Q1 (b) ii • Q1 (b) iii • Q1 (c) • Q2 (a) i • Q2 (a) ii • Q2 (a) iii • Q2 (b) i • Q2 (b) ii • Q2 (b) iii • Q2 (c) • Q3 • Q4 (i) • Q4 (ii) • Q4 (iii) • Q4 (iv) • Q4 (v) • Q4 (vi) • Q5 • Q6 • Q7 (i) • Q7 (ii) • Q7 (iii) • Q8 (i) • Q8 (ii) • Q8 (iii) • Q9 •
Question 07 (ii)
A particle is moving in the (x,y)-plane along the curve . As it passes through
the point P = (2, 4), its y coordinate changes at a rate of 8 units/sec.
ii) What is the rate of change of the particle's distance to the origin at this instant?
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Using the Pythagorean Theorem, we see that
Differentiate this function.
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As discussed in the hint,
From the previous part, we have that
and we are given that
and so plugging in the point , and (D must be positive) we have
completing the question. All answers in the last line are equivalently correct.
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