# Confusion regarding ball bouncing off a wall with respect to Newton's Third Law

This is more of a confirmation post whether my ideas are correct or not.

Suppose a ball of mass $$5 kg$$ travelling with uniform velocity $$5 ms^{-1}$$ through vacuum hits a block of mass $$200kg$$ with force $$F_a$$. The wall gets an acceleration of $$0.5ms^{-2}$$. So the force acting on the block, i.e., $$m_{block}a_{block}=200×0.5 N=100N$$ Now I think the block will apply an equal reaction force on the ball $$F_r$$ which is equal to $$ma$$ as well, except that the mass of the ball is $$5kg$$, so the acceleration produced is $$a_{ball}=\frac {F_{r}}{m_{ball}} = \frac{-100}{5}=-20ms^{-2}$$

Now considering the equation of motion, we get $$v=u+at$$ the new velocity of the ball is: $$v=5-200t$$ right? So now if the ball is in vacuum, and energy loss due to heat and sound is $$0$$, If my above statements are correct, then the ball should have a retardation right? Like as soon as it touches the block, it slows down and eventually comes to rest. The retardation still acts on it so it now gains a velocity backwards. It will now keep moving backwards with an acceleration $$200ms^{-2}$$ right?

Now in practical situations, the ball will lose some energy on hitting the wall because of friction and heat. Now after the ball gets a negative acceleration, it will try to move back, but I have noticed that the ball won't move back much and fall down.

• Is it because of gravity pulling it back, and resistance provided by air, which counteracts the movement of the ball and causes it to slow down and eventually stop?

• Does this mean that it is not necessary that the object has to be compressible, as in a rubber ball, in order to bounce, as they follow Newton's Third Law anyways?

• What would have happened if the ball was accelerating as well? Would the final motion of the ball be in the direction of the net acceleration?

Search up "impulse" $$\int F dt$$ = Change in momentum