Question

A force F=VxA is exerted on a particle in addition to
the force of gravity, where v is the velocity of the particle
and 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?​

Answer 1

Mass of the particle is m.

Consider that the particle is projected with velocity v , perpendicular to the direction of A vector.

So the force on the particle is in upward direction,

(vector) F = (vector)v x (vector)A

F = v sin90° = vA          ......(i)

A is the magnitude of the (vector)A.

Gravitational force acting on the particle in downward direction is, = mg---(ii)

If F is equal to the gravitational force then the particle moves undeflected.

vA=mg

v=$\frac{mg}{A}$

is the minimum velocity.

Answer 2

》》Answer《《

see the attached image for your answer