The total momentum is the same before the bottle is opened and after the cork pops up. Initial the momentum is zero so that this means

` 0 = M*v_1 +mv_2` or equivalent `v_2 =-(M/m)*v_1`

For the force that acts on the bottle we can write the theorem of momentum...

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The total momentum is the same before the bottle is opened and after the cork pops up. Initial the momentum is zero so that this means

` 0 = M*v_1 +mv_2` or equivalent `v_2 =-(M/m)*v_1`

For the force that acts on the bottle we can write the theorem of momentum variation:

`F = (M*v_1)/t `` ` or rearranging the terms `F/M =v_1/t` which means

`a_1 =v_1/t`

The motion of the bottle is uniform decelerated so that one can write

`d = v_1*t -(a*t^2)/2 =v_1*t -(v_1/t)*t^2/2 =v_1*t-(v_1*t)/2=(v_1*t)/2`

Thus the initial speed of the bottle is

`v_1 =(2*d)/t = (2*0.22)/0.61 =0.72 m/s`

This gives for the speed of the cork the value

`v_2 =(M/m)*v_1 =500*0.72 =360.66 m/s`

Now, the cork will follow a parabolic falling trajectory. On the vertical axis there is free fall (uniform accelerated motion). Since the diameter of the bottle is 14 cm the falling time is

`(D/2) =(g*t_2^2)/2`

`t_2 =sqrt (D/g)=sqrt(0.14/9.81) =0.1195 s`

On the horizontal axis there is uniform motion with initial speed ` ` `v_2`

The total horizontal distance that the cork will travel is

`s = v_2*t_2 =360.66*0.1195 =43.02 m =43 m`

**The cork will land on the table at 43 m from its original position.**

**Further Reading**