1. An object with mass m moves vertically under constant gravitational force through a medium that exerts a resistance with magnitude proportional to the speed of the obj ect. Assume that the initial velocity is no and the initial altitude is yo. A) Find the velocity of the object as a function of t B) Find the terminal velocity (i.e., tlim v(t)). C) Find y(t), where y(t) represents the altitude of the object at any time t. 2. Suppose an object with initial temperature To is placed in a sealed container, which is in turn placed in a medium with temperature Tm. Let the initial temperature of the container be SO. Assume that the temperature of the object does not affect the temperature of the container, which in turn does not affect the temperature of the medium. (These assumptions are reasonable, for example, if the object is a cup of coee, the container is a house, and the medium is the atmosphere.) A) Assuming that the container and the medium have distinct temperature decay constants k and km respectively, use Newton's law of cooling to nd the temperatures 505) and T0?) of the container and object at time t. B) Assuming that the container and the medium have the same temperature decay constant k, use Newton's law of cooling to nd the temperatures 5' (t) and T0?) of the container and object at time t. C) Find the limiting values of temperatures 30:) and T(t)