# Science:Math Exam Resources/Courses/MATH102/December 2017/Question 15 (b)

MATH102 December 2017
Other MATH102 Exams

### 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 ${\textstyle t}$ seconds is

${\displaystyle h(t)=3+3\sin \left({\frac {5}{3}}t\right)}$
centimetres.

(b) If the grasshopper can repeatedly reach a vertical acceleration of ${\displaystyle 5}$ centimetres per second squared, it can free itself. Can the grasshopper free itself? (Remember to justify your answer.)

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