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 given by the following where g is the acceleration due to gravity and c is a positive constant describing air resistance.
v=((mg)/c) \(1-e^(-(ct)\/m)\)
(a) Calculate the following.
lim_(t->infinity) v= __________
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.
4)It is the speed the object reaches before it starts to slow down.
(b) For fixed t, use l'Hospital's Rule to calculate the following.
lim_(c->0**+) v= ___________
What can you conclude about the velocity of a falling object in a vacuum?
1)The speed has nothing to do with the elapsed time. The heavier the object is the faster it will fall.
2)The speed is jointly proportional to the time and the mass. The longer the object falls and the heavier it is the faster it will fall.
3)The speed is proportional to the elapsed time. It doesn't depend on the mass. The longer the object falls the faster it will fall.