calculus help check and help

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if an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account is

v= mg/c(1-e^(-ct/m)) where g is the acceleration due to gravity and c is a positive constant describing air resistance.

a) calculate lim t->infinity (v.
answer: mg/c

----->what is the meaning of this limit


1)it is the time it takes the object to reach its maximum speed.

2)it is the speed the object approaches as time goes on.

3)it is the time it takes for the object to stop.


b) for fixed t us l'hospital's rule to calculate lim c->0^+ (v).

answer : tg


----->what can you conclude about the velocity of a falling object in a vacuum.


1)the velocity of a falling object in a vacuum is directly proportional to the amount of time it falls.

2)the heavier the object is the faster it will fall in a vacuum.

3)an object falling in a vaccuum will accelerate at a slower rate than an object not in a vacuum.

  • calculus help check and help -

    a) calculate lim t->infinity (v.
    answer: mg/c

    ----->what is the meaning of this limit
    ==============================
    It is the "terminal velocity" (Google that) which is the speed where the drag force equals the weight. One uses a parachute so that one's terminal velocity is low enough to hit the ground without quite dying.

    So
    2)it is the speed the object approaches as time goes on.

    AND
    In a vacuum, c = 0 so terminal velocity is undefined.

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