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Two objects of masses `100g` and `200g` are moving along the same line in the same direction with velocities of `2m//s` and `1m//s`, respectively. They collide and after the collison, the first object moves at a velocity of `1.67 m//s` in the same direction. Determine the velocity of the second object.

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In order to solve this problem, we will first calculate total momentum of both the objects before and after the collision.
Momentum of first object (before collision)=Mass of first object`xx`Velocity of first object
`=100/1000kgxx2ms^(-1)`
`0.1kgxx2ms^(-1)`
`=0.2 kg ms^(-1)`
Momentum of second object (before collision) = Mass of second object`xx` Velocity of second object
`=200/1000kgxx1ms^(-1)`
`=0.2kgms^(-1)`
Total momentum = 0.2 + 0.2
(before collision)=-04 kg `m s^(-1)`
(b) After collision, the velocity of first object of mass 100 g becomes 1.67 m `s^(-1)`. So,
Momentum of first object (after collision)=`100/1000kgxx1.67ms^(-1)`
`=0.1kgxx1.67ms^(-1)`
`=0.167kgms^(-1)`
After collision, suppose the velocity of second object of mass 200 g becomes v`ms^(-1)`. So,
Momentum of second object (after collision)=`200/1000kgxxvms^(-1)`
`=0.2kgxxvms^(-1)`
`=0.2vkgms^(-1)`
Total momentum (after collision)=0.167+0.2 v
Now, according to the law of conservation of momentum :
Total momentum before collision=Total collision after collision
That is, 0.4=0.167+0.2v
0.2v=0.4-0.167
0.2v=0.233
`v=0.233/0.2`
`v=1.165ms^(-1)`
Thus, the velocity of second object is 1.165 metres per second.

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