Force perpendicular to velocity In a recent physics class, I was told that force can change the direction of velocity as well as its magnitude simultaneously. My professor drew a diagram in which a particle is moving along a horizontal line and is acted upon by a force at angle $O$ with horizontal velocity. He said that component of force in downward direction will change the direction of horizontal velocity while the component of force along velocity will increase its speed which arose following doubts in my mind-
$1$  The perpendicular component of force will change the direction of velocity since instantaneous acceleration due to this component will be perpendicular to it, for an instant only. I want to understand what will be state of motion of this body after this instant.
$2$  if instantaneous acceleration is perpendicular to velocity then the direction of velocity changes in this instant. Now in projectile motion, instantaneous acceleration $g$ is perpendicular to the horizontal component of velocity, therefore by the above reasoning it should also change its direction.
All this has left me confused. Can anyone please help me to understand or tell me where I'm lagging?
 A: Have a look at Newton's 2nd law, $$\sum F=ma. $$
In the perpendicular direction there is no speed. Meaning, when the object is moving horizontally it is not at the same time moving upwards. There is a horizontal speed component, $v_x$, but no upwards speed component, $v_y=0$, $$v=(v_x, 0). $$
If a force then pulls upwards, then apply Newton's 2nd law along this upwards direction. The upwards force will cause an upwards acceleration.
This upwards acceleration will in turn cause an upwards speed component, $v_y$. We now have $$v=(v_x, v_y), $$ which corresponds to a velocity that isn't horizontal anymore. The upwards force has caused the velocity to tilt upwards and have an angle.
Whenever a force is perpendicular, the above will happen. This also applies to gravity, which is why any object that you throw sideways, horizontally, gains a vertical speed component and begins falling down. We call this projectile motion. In special cases the force turns as well so that it always is perpendicular - after having tilted the velocity a bit, the force itself turns so it is perpendicular to this ned velocity. This is the case when you drive around a roundabout where you are constantly turning - and this is the case for a satellite in circular orbit where gravity always points down. Then we have perfect circular motion, meaning constant turning.
A: 
I want to understand what will be state of motion of this body after [the first] instant.

That depends on the nature of the force. if the force is acting in a constant direction (e.g. gravity) then after the first instant there is a component of the force parallel to the velocity of the object (because the direction of the object's velocity has changed). This component will accelerate the object. On the other hand, if the force is always perpendicular to the object's velocity (e.g. an object on the end of a string) then it will continue to change the direction of the object's velocity, but not its magnitude.

In projectile motion, instantaneous acceleration g is perpendicular to horizontal component of velocity, therefore by above reasoning it should also change it's direction.

Yes, and it does. The direction of an object moving under gravity (projectile motion) is, in general constantly changing, as the object moves in a parabola. There is just one exception to this - if the object is initially moving straight up (or down) then its direction of motion does not change because there is no component of gravity perpendicular to its velocity.
