Can someone explain me the logic behind this?

Question

At each moment during its flight, a projectile has a velocity  and an acceleration . The components of these variables are:

v_x = x component of the velocity

v_y = y component of the velocity

a_x = x component of the acceleration

a_y = y component of the acceleration.

Which of these components remain constant throughout the motion? Assume that air resistance is absent.

Only a_x and a_y are constant.v_x, a_x and a_y are constant.  

Only v_x and a_y are constant.

None of the variables is constant.

v_y, a_x and a_y are constant.

Answer 1

Hi Giselle,

When we think of an object's motion through space we can look at each dimension separately. If there is a force like gravity that always pulls objects downward, it cannot have any effect on the horizontal movement.

When an initial force propels an object at an angle, it will have some vertical or y component and some horizontal or x component. Similarly, according to Newton's first law, an object will accelerate if there is a force. Since you are told to ignore air resistance in this problem, you will have no horizontal acceleration. And with no horizontal acceleration, the object will always move with its initial horizontal velocity. In the vertical direction, we cannot ignore that gravity is a force and with force comes acceleration. The vertical velocity must change because it is being accelerated.

So, according to the information told to you in the problem, only one acceleration and one velocity would be constant.

I hope that helps! Let me know if you have any other questions.