Let us consider a boat which moves with a velocity $v_{b w}=5 \mathrm{~km}$ $\mathrm{h}^{-1}$ relative to water. At time $t=0$, the boat passes through a piece of cork floating in water while moving downstream. If it turns back at time $t=t_{1}$, when and where does the boat meet the cork…

Question

Let us consider a boat which moves with a velocity $v_{b w}=5 \mathrm{~km}$ $\mathrm{h}^{-1}$ relative to water. At time $t=0$, the boat passes through a piece of cork floating in water while moving downstream. If it turns back at time $t=t_{1}$, when and where does the boat meet the cork again? Assume $t_{1}=30 \mathrm{~min}$.

Aicharya · Accepted Answer

Time of travelling of boat from $A$ to $B\left(t_{1}\right)$ and then $B$ to $C$ $\left(t_{1}^{\prime}\right)=$ time of moving the cork from $A$ to $C$. Velocity of boat from $A$ to $B$ $\vec{v}_{b, w}+\vec{v}_{w}=(5+u) \mathrm{km} \mathrm{h}^{-1}$ And velocity of boat from $B$ to $C$ $\vec{v}_{b, w}+\vec{v}_{w}=(5-u) \mathrm{km} \mathrm{h}^{-1}$ Distance moved by boat in time $t_{1}$ $\begin{array}{l} A B=(5+u) t_{1} \ \text {And distance moved by boat in time } t_{1}^{\prime}=\mathrm{BC}=(5-u) t_{1}^{\prime} \end{array}$ Distance moved by cork during this time $A C=u\left(t_{1}+t_{1}^{\prime}\right)$ But $A B=A C+B C$ $\begin{array}{l} (5+u) t_{1}=u\left(t_{1}+t_{1}^{\prime}\right)+(5-u) t_{1}^{\prime} \ 5 t_{1}=5 t_{1}^{\prime} \Rightarrow t_{1}^{\prime}=t_{1}=30 \mathrm{~min} \end{array}$ Hence, the cork meets the boat again after $1 \mathrm{~h}$ ^

Let us consider a boat which moves with a velocity \(v_{b w}=5 \mathrm{~km}\) \(\mathrm{h}^{-1}\) relative…

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