Science:Math Exam Resources/Courses/MATH110/December 2015/Question 05 (c)

MATH110 December 2015

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Question 05 (c)
A ball is floating on the surface of the sea. The ball’s height $h$ (in m) above the sea floor at time $t$ (in s) is given by $h(t)=5+0.1\sin(2t).$ Answer the questions below. Evaluate all function values and provide justification for your claims. Include units. (c) Is the ball moving up or down at $t={\frac {\pi }{6}}$ ? Explain.

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!

Hint
When a ball is moving up, it means that $h(t)$ is increasing. On the other hand, when a ball is moving down, it corresponds that $h(t)$ is decreasing. Recall that when $h'(t)>0$ on $(a,b)$, $h$ is increasing on the interval.

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Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. According to the Hint, it is enough to check the sign of $v=h'$ at $t={\frac {\pi }{6}}$. From the part (b), we have $v\left({\frac {\pi }{6}}\right)=0.1>0$, and therefore, $h$ is increasing at $t={\frac {\pi }{6}}$. Answer : $\color {blue}moving\ up$