A force $\bar{F} = \bar{V} \times \bar{A}$ is exerted on a particle in addition to the force of gravity, where $\bar{V}$ is the velocity of the particle and $\bar{A}$ is a constant vector in the horizontal direction. The minimum speed of a particle of mass $3 k g$ be projected, so that it continuous to move undeflected with a constant velocity is $x g / A$ . Then $x g / A$ is (consider the plane of the ground as xy plane)

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Detailed Solution

As $\bar{v}$ is constant , $\bar{a} = 0$

$∴ {\bar{F}}_{n e t} = 0$

$\bar{F} + m \bar{g} = \bar{0}$

$\bar{V} \times \bar{A} + m \bar{g} = \bar{0}$

$\bar{V} \times \bar{A} = - m \bar{g}$

$= - 3 \bar{g}$

$| \bar{V} \times \bar{A} | = | - 3 \bar{g} |$

$V A \sin θ = 3 g$

$V = \frac{3 g}{A \sin θ}$

If $\sin θ = 1 \Rightarrow V$ is minimum

$∴ V_{\min} = \frac{3 g}{A}$

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