Question

Some passengers on an ocean cruise may suffer from motion sickness as the ship rocks back and forth on the waves. At one position on the ship, passengers experience a vertical motion of amplitude 1.4 m with a period of 14 s .
A. What is the maximum acceleration of the passengers during this motion?B. What fraction is this of g?

Answer 1

Answer:

0.28198 m/s²

0.02874

Explanation:

A = Amplitude = 1.4 m

T = Time period = 14 s

g = Acceleration due to gravity = 9.81 m/s²

Acceleration is given by

$a=\omega^2A\\\Rightarrow a=\left(\frac{2\pi}{T}\right)^2A\\\Rightarrow a=\left(\frac{2\pi}{14}\right)^2\times 1.4\\\Rightarrow a=0.28198\ m/s^2$

The maximum acceleration of the passengers during this motion is 0.28198 m/s²

Dividing this value by g

$\frac{a}{g}=\frac{0.28198}{9.81}\\\Rightarrow a=0.02874g$

The fraction of g is 0.02874