(D) The power $P$ delivered by a force $\vec{F}$ to an object moving with velocity $\vec{v}$ is given by the dot product of the force and velocity vec

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(D) The power $P$ delivered by a force $\vec{F}$ to an object moving with velocity $\vec{v}$ is given by the dot product of the force and velocity vectors: $P = \vec{F} \cdot \vec{v}$.Given:$\vec{v} = 7 \hat{i} + 2 \hat{j} - 5 \hat{k} \text{ m/s}$$\vec{F} = 9 \hat{i} + 3 \hat{j} - 3 \hat{k} \text{ N}$Calculating the dot product:$P = (9 \hat{i} + 3 \hat{j} - 3 \hat{k}) \cdot (7 \hat{i} + 2 \hat{j} - 5 \hat{k})$$P = (9 \times 7) + (3 \times 2) + (-3 \times -5)$$P = 63 + 6 + 15$$P = 84 \text{ W}$

Class 11 Physics Work, Energy, Power and Collision Power

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$A$ motor boat is moving in a river with velocity $\vec{v} = 7 \hat{i} + 2 \hat{j} - 5 \hat{k} \text{ m/s}$. If the flow of water offers a resistive force $\vec{F} = 9 \hat{i} + 3 \hat{j} - 3 \hat{k} \text{ N}$, then the power of the boat is: (in $\text{ W}$)

AP EAMCET 2023 All AP EAMCET

A
$13$
B
$69$
C
$12$
D
$84$

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$A$ motor boat is moving in a river with velocity $\vec{v} = 7 \hat{i} + 2 \hat{j} - 5 \hat{k} \text{ m/s}$. If the flow of water offers a resistive force $\vec{F} = 9 \hat{i} + 3 \hat{j} - 3 \hat{k} \text{ N}$, then the power of the boat is: (in $\text{ W}$)

Similar Questions

$A$ weight lifter lifts $300 \ kg$ from the ground to a height of $2 \ m$ in $3 \ s$. The average power generated by him is $... \ W$.

From a waterfall,water is pouring down at the rate of $100 \,kg/s$ on the blades of a turbine. If the height of the fall is $100 \,m$,the power delivered to the turbine is approximately equal to .......... $kW$.

$A$ body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement $s$ is given as a function of time $t$ as:

$A$ body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to

$A$ force $\vec{F} = (4 \hat{i} + \hat{j} - 2 \hat{k}) \text{ N}$ acting on a body maintains its velocity at $\vec{v} = (2 \hat{i} + 2 \hat{j} + 3 \hat{k}) \text{ m s}^{-1}$. The power exerted is $..... \text{ W}$.

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