Chapter 4, Problem 190RE

To determine

To write an equation modeling the motion of bobber, where the high point corresponds to the time $t=0$ .

Answer to Problem 190RE

The equation of motion of fishing bobber is $d=7\cos \pi t$ .

Explanation of Solution

Given information:

Fishing bobber is oscillating in simple harmonic motion caused by waves .Bobber moves a total of $7$ inches from its high point to its low point and returns to its high point every $2$ seconds.

Calculation:

Simple harmonic motion of a body is given by

  $d=a\sin \omega t$ or $d=a\cos \omega t$

Total distance that bobber moves from its high point to its low point : $\left|a\right|=7$

Total time bobber takes to returns to its high point is $2$ seconds.

  $\begin{array}{l}T=\frac{2\pi }{\omega }\\ 2=\frac{2\pi }{\omega }\\ \omega =\pi \end{array}$

The equation contain cosine term since the high point of fishing bobber is at $t=0$

Therefore, equation of motion of fishing bobber is given by

  $d=7\cos \pi t$