The front windscreen of a car is inclined at an angle of 30 degrees with the horizontal. Hailstones fall vertically downwards with a speed of 5√3 m/s. Find the speed of the car so that:
a) It avoids hailstones completely.
b) Hailstones appear to move horizontally.
c) Hailstones fall at an angle of 60 degrees.
d) It matches the speed of hailstones.