An automobile is traveling at a speed of 80 km/h through heavy rain. The raindro

Question

An automobile is traveling at a speed of 80 km/h through heavy rain. The raindrops are falling vertically at 10 m/s, and there are 7.0x10^-4 kg of raindrops in each cubic meter of air. For the following calculations assume that the automobile has the shape of a rectangle box 2.0 m wide, 1.5 m high, and 4.0 m long.
a) At what rate (in 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 is the horizontal drag force that the impact of the raindrops exerts on the automobile?

Explanation / Answer

automobile speed=80 km/hr=22.22m/s speed in downward dircetion=10m/s speed of rain relative to car in front direction=22.22m/s a) front area=2*1.5=3m^2 top area=4*2=6m^2 rainstrike front=7.0x10^-4 kg*3*22.22 =.0466kg/sec rainstrike top=7.0x10^-4 kg*6*10 =.042kg/sec b)rate of momentum change=momentum/sec= .0466*22 =1.0252 drag force=momentum change/sec of car rate of momentum change of rain=rate of momentum change of car drag force=1.0252N

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