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.
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Answer

`10 sqrt(3) m s^-1`.

Explanation

For the driver to observe, the hailstones move vertically upward after the elastic collision.
Let the velocity of hailstone w.r.t. car be `vec v_(h,c)`
Then `vec v_h = vec v_(h,c) + vec v_c`
`(vec v_h)_x = (vec v_(h,c) + vec v_c)_x`
`vec v_h = vec v_(h,c) + vec v_c`
`(vec v_h)_x = (vec v_(h,c) + vec v_c)_x`
But `(vec v_h)_x = 0`, since hailstones fall vertically down.
`rArr (vec v_h)_x = -(v cos 30^@) rArr |vec v_c|_x = |vec v_(h,c)|_x`
Now, `(vec v_h)_y = (vec v_(h,c) + vec v_c)_y`
Since `(v_h)_y = -10 ms^-1 , (v_c)_y = 0 rArr -10 = -V sin 30^@ + 0`
`V sin 30^@ = 10 rArr V = 20 ms^-1`
`(vec v_c)_x = V cos 30^@ = 20 xx (sqrt(3))/(2) = 10 sqrt(3) ms^-1`
`vec v_c = 10 sqrt(3) ms^-1`.
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