University:
Georgia Southern University
Course:
MATH 3230 | Ordinary Differential Equations
Academic year:

2024
Views:

443

Pages:

2
Author:

Jalen W.

An Object in Freefall We say that an object is in freefall if it dropped from a height and the only forces acting on it are gravity and wind resistance. dv = mg − kv dt dv m + kv = mg dt dv k + v =g dt m Z m kv mg v (t) = e −kt/m g · e kt/m dt mg + Ce −kt/m k mg v (0) = + C = v0 k mg mg −kt/m v (t) = + v0 − e k k v (t) = Example–Terminal Velocity An object cannot accelerate towards the ground forever. Eventually, air resistance stabilizes the speed of the object. Find the terminal velocity of an object in freefall in terms of m, g , and k. Solution: vterminal = lim v (t) = t→∞ mg k

An Object in Freefall

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