I need to understand these questions in details

The object falls 5 meters changing E(potential) to E(kinetic), then it goes back up changing E(kinetic) to E(potential). Still it hasn't reached its previous height so there will still be E(kinetic) left. The difference in height from beginning to end is 3 meters: 5 meters (beginning)- 2 meters (end)=3 meters.

17. The red ball will bounce back after collision and move in the same direction the yellow ball went previously. This means the speed must be negative and only one of the answers is negative so answer d seems logical.

=>(Red)     (Yellow)<=

(Red)(Yellow)

(Red)<=  =>(Yellow)

The red ball will move in the opposite direction so negative speed. So answer D should be correct.

24.

E(potential)=m*g*h=m*9.81*(5-2)=m*29.43

E(kinetic)=1/2*m*v^2

E(kinetic)=E(potential)

1/2*m*v^2=m*29.43

v^2=29.43*2=58.86

v=58.86^(1/2)=7.67

The correct answer is C

I want more explanation for question 24 

In a closed system there is no loss of energy. The potential energy is the energy every object has that can be released by letting it fall, the potential energy will be transformed to kinetic energy (speed).

This means all the energy released by dropping 3 meters (5-2) will go towards kinetic energy. The formula for potential energy is E(potential)=mass*gravitational unit*height, the formula for kinetic energy is E(kinetic)=1/2*mass*velocity^2.

Since E(potential) becomes E(kenetic) you can equate these two kinds of energy, so E(potential)=E(kinetic) (more precisely E(potential_begin)-E(potential_end)=E(kenetic)). The mass is unknown but appears in both formulas so you remove it from both sides, the result is: height (difference in height)*gravitational unit=1/2*velocity^2 which grants you the answer to your question.

fine .. my last question .. why you put the heights 3 m ! 

Thank you Honga 

now its very clear