Science:Math Exam Resources/Courses/MATH102/December 2017/Question 15 (b)
• Q1 • Q2 • Q3 • Q4 • Q5 • Q6 • Q7 (a) • Q7 (b) • Q7 (c) • Q8 • Q9 (a) • Q9 (b) • Q9 (c) • Q10 (a) • Q10 (b) • Q10 (c) • Q10 (d) • Q11 (a) • Q11 (b) • Q12 (a) • Q12 (b) • Q12 (c) • Q12 (d) • Q13 (a) • Q13 (b) • Q13 (c) • Q13 (d) • Q14 (a) • Q14 (b) • Q15 (a) • Q15 (b) • Q16 •
Question 15 (b) 

A grasshopper caught in a spiderweb rhythmically kicks its legs, causing the web to bounce up and down. The height of the grasshopper (in cm) after seconds is centimetres.
(b) If the grasshopper can repeatedly reach a vertical acceleration of centimetres per second squared, it can free itself. Can the grasshopper free itself? (Remember to justify your answer.) 
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 

The acceleration is the second derivative of the displacement (height). 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

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, let us compute the acceleration, which is the second derviative: applying the chain rule, we get As varies, we see that oscillates between and . Since , the grasshopper can repeatedly (recall that the function is periodic of period from part (a)) reach a vertical acceleration of . So the grasshopper can free itself.
Answer: 