motion in one dimension

The most simple way to solve this is by comparing the energy of the balls: (I assume that the balls has the same mass, and the speed isn't affected by air friction)
At the beginning, both balls have the same kinetic energy (K=(1/2)*m*v2) and the same potential energy (U=mgh) so their total energy is the same.
At the end, just before they hit the ground, both balls have zero potential energy (since the height is 0) so all of their energy was transformed into kinetic energy. Because at the beginning the energies of the balls were the same, finally the energy of the balls will also be the same. And because the balls have only kinetic energy, we have: (1/2)*m*(V1)2=(1/2)*m*(V2)2 <=> V1=V2 so the answer is c).

Remember: If you throw a ball upwards with vi speed, it will return to you with vi speed. That happens because when you throw your ball up, you give it some kinetic energy. The ball will momently have zero speed (at it's higher point). there, all the kinetic energy was transformed into potential energy. When the ball returns to you, the ball will lose this potential energy. This potential energy was transformed again into the same amount of kinetic energy. (again, if we assume that we have no friction.)

thank you, but if you dont mind how will i  know when i have to use  (K=(1/2)*m*v2)?


thanks once again for the help!

A moving object in a gravitational field has two kind of energies:
1)kinetic energy (K=(1/2)*m*v2 for non-rotating objects. If the object is also rotating there are other formulas that describe kinetic energy.)
2) Potential energy. The potential energy is the "capability" of the object to acquire more kinetic energy. For example, if you have an object on a table, it has potential energy because if you let the object fall, it will aquire some kinetic energy.

Practically when you have a moving and non-rotating object: The kinetic energy is K=(1/2)*m*v2 and the potential energy is U=mgh (h is the height above the surface of the earth. That is not necessary, but usually, due to simplicity, we assume that at the surface of the earth we have U=0.)

The total energy of the object is E=U+K and it remains constant if the object does not interact with other objects (e.g. collide with another object) or generally if there isn't any force, apart from gravity, that is applied to the object. If these conditions apply, then the reduction of kinetic energy results in an increase of potential energy, and the reduction of the potential energy results in an increase of the kinetic energy.

(The above applies to moving objects in the gravitational field of Earth, where the object does not interact with other fields, like electrical or magnetic fields.)

The best way to learn how to use these formulas is to solve exercises. So, if you encounter any problem or you have questions, you can ask (preferably by starting a new topic)