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MATHEMATICS - CASE STUDY

    Introduction


Acceleration of a Typical
Raindrop Over Time
Click here to view movie (30.0 KB)

 

As raindrops fall, their surface enlarges which increases the resistance to accelerate. This acceleration can be modeled as

     

where t is time.

Assume the rain starts 800 meters above the ground and has an initial velocity of 10 m/s.

    Questions

 

  How long does it take the raindrop to reach the ground?
     
    Approach


 
  • The velocity is the antiderivative (integral) of the acceleration.
  • The distance is the antiderivative (integral) of the velocity.