In addition to the force of gravity, a force F = v A acts on a particle, where v represents the particle's velocity and A is a constant horizontal vector. Determine the minimum speed at which a particle of mass m must be projected to ensure it travels undeflected at a constant velocity.

Step-by-step solution

For the particle to move undeflected at a constant velocity, the net force acting on it must be zero. The forces acting on the particle are the gravitational force m g and the given force F = v A . Equating the net force to zero gives: m g + v A = 0 v A = -m g Taking the magnitude on both sides yields: v A = mg where is the angle between the velocity vector v and the constant horizontal vector A . To minimize the speed v , must be maximized. The maximum value of is 1 , which occurs when = 90^ . Substituting = 1 giv