A force is exerted on a particle in addition to the force of gravity, where 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?

Since we need equilibrium,

Velocity must be in direction perpendicular to plane in which gravity acts.

Thus, , θ is the angle between A vector and velocity of the particle.

∴

Now, for the velocity to be minimum, sin θ must be maximum,

and maximum value of sinθ=1

∴ minimum velocity of the particle