The front wind screen of a car is inclined at an 60^@ with the vertical. Hailstones fall vertically downwards with a speed of 5 sqrt(3) ms^-1. Find the speed of the car so that hailstones are bounced back by the screen in vertically upward direction with respect to car. Assume elastic collision of hailstones with wind screen.

The front wind screen of a car is inclined at an 60^@ with the vertica

1.	The front wind screen of a car is inclined at an 60^@ with the vertical. Hailstones fall vertically downwards with a speed of 5 sqrt(3) ms^-1. Find the speed of the car so that hailstones are bounced back by the screen in vertically upward direction with respect to car. Assume elastic collision of hailstones with wind screen.
Answer» Solution :Let `vec v_c = v_0 hat i, vec v_(h//c) = -(v_1)/(2) hat J - v_1 (sqrt(3))/(2) hat i` `vec v_h = -(v_1)/(2) hat j + (v_0 - v_1 (sqrt(3))/(2)) hat i` Now `v_0 - v_1 (sqrt(3))/(2) = 0 rArr v_1 = (2 v_0)/(sqrt(3))` Also `((v_1)/(2))^2 + (v_0 - v_1 (sqrt(3))/(2))^2 = (5 sqrt(3))^2` `rArr v_1^2 = 75 xx 4 rArr (4 v_0^2)/(2) = 75 xx 4 rArr v_0 = 15 ms^-1`. .