Question

A force

F→=v→×A→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 without being defelected and with a constant velocity?

Answer 1

Given :

F=uz x A and mg are acting on the object

For a particle to move with a constant velocity without being deflected the the net force acting  on the object must be zero.

ux A+mg=0

uxA=-mg

because ux A is to the place containing u and Av should be in xz plane.

So

uA sin q=mg

u=mg/Asinθ

u will be minimum when sinθ=1

θ=90°

umin= mg/A along Z axis.

Answer 2

Given :

F=uz x A and mg are acting on the object

For a particle to move with a constant velocity without being deflected the the net force acting  on the object must be zero.

ux A+mg=0

uxA=-mg

because ux A is to the place containing u and Av should be in xz plane.

So

uA sin q=mg

u=mg/Asinθ

u will be minimum when sinθ=1

θ=90°

umin= mg/A along Z axis.