A stone is thrown from the top of a cliff with speed v at an angle above the horizontal. Air resistance is negligible and the acceleration of free fall is g. Why is the horizontal velocity of the stone as time t after the stone has been thrown v*cos(theta)

The horizontal velocity of the stone is given by its initial horizontal velocity component, which is v*cos(theta). This is because there is no horizontal force acting on the stone after it has been thrown, so its horizontal velocity remains constant. The only force acting on the stone in the horizontal direction is its initial velocity component, which is v*cos(theta).