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 (iii)
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.
iii) What is the rate of change of the angle between the positive x-axis and the
line connecting the origin and the particle?
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!
We need to relate the angle with the x and y coordinates. Try using
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Taking derivatives with respect to time gives
From the previous parts, we have that
and we are given that
and so plugging in the point into the triangle, we see that
Using all this information, we plug in the point and see that
and this completes the question.
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