A molecule in a gas container hits a horizontal wall with speed `200 ms^(-1) and " angle " 30^(@)` with the normal , and rebounds with the same speed . Is momentum conserved in the collision ? Is the collision elastic or inelastic ?

Explanation

Suppose the mass of the molecule be m and that of wall be M. The wall remains at rest due to its large mass and the molecule collide with wall at initial velocity and its initial momentum `P_(i)= m vec(u)` . Before collision the X - component of ` m vec(u)` of mlecule = `mv cos theta`
` = - mxx 200 xx cos 30^(@)`
`= - 100 xxsqrt(3)" " [ :. cos 30^(@)=(sqrt(3))/2]`

The y- component of `m vec (u)` of molecule = `"mu"sin theta`
` = m xx 200 xx sin 30^(@)=100 m `
After collision ,
x - component of m `vec(v)` of molecule .
` = mv sin theta`
` = m xx 200 xx cos 30^(@)`
` = 100sqrt(3)` m
y - component of `m vec(v)` of molecule ,
` m xx 200 xx sin 30^(@)`
= 100 m and wall remains at rest so its momentum is zero .
Now, the value of `vec(u) and vec(v)` are same and mass is also same . So, kinetic energy `1/2 "mu"^(2) and 1/2mv(2)` is also same. So, kinetic energy `1/2 "mu"^(2) and 1/2 mv^(2)` is also same and momentum before collision = momentum after collision . Hence , this collision is elastic collision .