Under Certain Assumptions, The Velocity V(t) Of A

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Under certain assumptions, the velocity v(t) of a falling raindrop at time t is given by the formula below, where g is the acceleration due to gravity and b is the terminal velocity of the raindrop. Find the limit as t approaches infinity of v(t). v(t) = b(1 - e^(-gt/b))

 

Answer No.1

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As t grows very large, the term exp[-gt/b] grows very small, and v(t)->b, so that b is the speed of the drop at large t and is called the terminal velocity

Answer No.2

Anonymous

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Another way:- The limit is b. When t ->infinity, e^(-infinity) -> 0, so v(infinity) = b(1 - 0) = b, that's why b is called the terminal velocity. The terminal velocity is a velocity that will not be exceeded.

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