A motor boat is moving in a river with velocity $\overrightarrow{\mathrm{v}}=7 \hat{\mathrm{i}}+2…

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
  1. $13 \mathrm{~W}$
  2. $69 \mathrm{~W}$
  3. $12 \mathrm{~W}$
  4. $84 \mathrm{~W}$

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} $

Asked in: AP EAMCET 2023 (18 May Shift 2)

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