A force vector F= vector v x vector A is exerted on a particle in addition to the force of gravity, where vector v is the velocity of the particle and vector A is a constant vector in the horizontal direction. With what minimum speed a particle of mass m be projected so that it continues to move undeflected with a constant velocity ?
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Since we need equilibrium,
\(v\times A+mg=0\)
Given that, \(\vec F=\vec u\times \vec A \) and \(\vec mg\) act on the particle.
Velocity must be in direction perpendicular to plane in which gravity acts.
Thus, \(v \times A=Av\,sin\theta,\,\theta\) is the angle between A vector and velocity of the particle.
So, \(v\times A =-mg\)
\(Av\,sin\theta=-mg\)
\(v=-\frac{mg}{A\,sin\theta}\)
Now, for the velocity to be minimum, sin θ must be maximum, and maximum value of sinθ=1
So, minimum velocity of the particle \(v=-\frac{mg}{A}m/s\)
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