Q124 / 160 · AP EAMCET 2023 (18 May Shift 2) · Physics
A motor boat is moving in a river with velocity $\overrightarrow{\mathrm{v}}=7 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-5 \hat{\mathrm{k}} \mathrm{ms}^{-1}$. If the flow of water offers resistive force $\vec{F}=9 \hat{i}+3 \hat{j}-3 \hat{k} \quad N$, then the power of the boat is
- A$13 \mathrm{~W}$
- B$69 \mathrm{~W}$
- C$12 \mathrm{~W}$
- Correct answerD$84 \mathrm{~W}$
Solution
Velocity of boat $V=7 \hat{i}+2 \hat{j}-5 \hat{k} \mathrm{~m} / \mathrm{s}$
$$
\begin{aligned}
& \text { Force, } F=9 \hat{i}+3 \hat{j}-3 \hat{k} \text { N } \\
& \text { Power, } P=? \\
& \quad P=F \cdot V \\
& =(9 \hat{i}+3 \hat{j}-3 \hat{k}) \cdot(7 \hat{i}+2 \hat{j}-5 \hat{k}) \\
& =63+6+15 \\
& P=84 \mathrm{~W}
\end{aligned}
$$
Hence, the correct answer is option: 'D'.