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. .

Hailstones falling vertically with a speed of 10 m s^-1, hit the wind

1.	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. .
Answer» Solution :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`. , .