Question

A boat at anchor is rocked by waves whose crests are $100\mathrm{m}$ apart and velocity is $25{\mathrm{ms}}^{-1}$. The boat bounces up once in every:

• A. $2500\mathrm{s}$
• B. $75\mathrm{s}$
• C. $4\mathrm{s}$
• D. $0.25\mathrm{s}$

Answer 1

The correct option is C

$4\mathrm{s}$

Step 1: Given data

The crests of a wave are $100\mathrm{m}$ apart which means:

Wavelength of a wave$=100\mathrm{m}$

Also the velocity of a wave$=25{\mathrm{ms}}^{-1}$

Step 2: Calculating the time taken by boat to bounce once

We know that the velocity of a wave is given by:

$$\begin{gathered} \mathrm{velocity}=\frac{\mathrm{wavelength}}{\mathrm{time}} \\ \Rightarrow \mathrm{time}=\frac{\mathrm{wavelength}}{\mathrm{velocity}} \\ \Rightarrow \mathrm{time}=\frac{100\mathrm{m}}{25{\mathrm{ms}}^{-1}} \\ \Rightarrow \mathrm{time}=4\mathrm{s} \end{gathered}$$

Therefore time taken by a boat to bounce once is equal to $4\mathrm{s}$.

Hence, option(C) is the correct answer.