Hailstones falling vertically with a speed of `10 m s^-1`, hit the wind screen (wind screen makes an angle `30^@` with the horizontal) of a moving car and rebound elastically. Find the velocity of the car if the driver finds the hailstones rebound vertically after striking.
.

Options

A. `10sqrt(3)m//s`
B. `20sqrt(3)m//s`
C. `10m//sec`
D. `(10)/(sqrt(3))sec`

Answer

A

Explanation

For the driver to observe the rain move vertically upward after the elastic collision, rain should come at an angle `30^(@)` with the horizontal `(` as clear from figure `)`
Let, velocity of rain `w.r.t.` car be `V_(m i c)`
`vec(V)_(R//G)=vec(V)_(R//C)+vec(V)_(C//G)`
`vec(V)_(R//G(x))=vec(V)_(R//C(x))+vec(V)_(C//G(x))`
But `vec(V)_(R//G(x))=0`, since rain fall vertically down .

`rArr vec(V)_(C//G(x))=-vec(V)_(R//C(x))=-(V cos 30^(@))`
`rArr |vec(V)_(C//G(x))|=V cos 30^(@) .... ....(i)`
Now, `vec(V)_(R//G(y))|vec(V)_(R//C(y))`
`rArr-10=-V sin 30^(@)+0`
`[` Since`,V_(R//G(y))=-10m//s,V_(C//G(y))=0]`
Substituting `V=20m//s` in equation `(i)`
`vec(V)_(C//G(x))=V cos 30^(@)=20xx(sqrt(3))/(2)=10sqrt(3)m//s.`
`:. vec(V)_(C//G(x))=10sqrt(3)hat(i)m//s.`