Horizontal drag due to rain

1. Nov 1, 2008

guardians

1. The problem statement, all variables and given/known data
An automobile is traveling at speed of 80 km/h through heavy rain. The raindrops are falling vertically at 10 m/s and there are 7*10^-4 kg of raindrops in each cubic meter of air. For the following calculations assume that the automobile has the shape of a rectangular box 2m wide, 1.5 high and 4m long.
a) At what rate (kg/s) do the raindrops strike the front and top of the automobile?
b) Assume that when a raindrop hits, it initially sticks to the automobile, although it falls off later. At what rate does the automobile give momentum to the raindrops? What horizontal drag force do the raindrops exert on the automobile?
2. Relevant equations
Fdt=d(mv)
mv+m1v'=(m+m1)v'' for inelastic colision

3. The attempt at a solution
Ok, so for a, I tried the following. The volume of air the upper and front parts of the automobile are going to go through is (w*h+w*l)$$\Delta$$t*vcar, for some interval $$\Delta$$t. If there are 7*10^-4kg of raindrops in a cubic meter, than the mass of raindrops hitting the car in that period is just (w*h+w*l)$$\Delta$$t*vcar*7*10^-4. This is by my textbook not correct. I also tried transforming to the reference frame of the car, but still didn't get the right answer.
I guess for b:
mcarvcar+$$\Delta$$mvrain=(m+$$\Delta$$m)vfinal
$$\Delta$$m=$$\Delta$$t*rate, than take take $$\Delta$$t$$\rightarrow$$0.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution