Suppose that an object of mass m is ejected downward with velocity v 0 over the

Question

Suppose that an object of mass m is ejected downward with velocity v0 over the surface of the planet whose gravitational constant is G. The atmosphere exerts resistance on the body according to (Resistive force = -kv) with constant of proportionality r. (All parameters are in cgs units.)

a) Find the formula for v(t).

b) Find the formula for the limiting velocity.

Assume that the object consists of a payload and a parachute. The payload is 80% of the total mass, and the parachute takes up the balance of the total mass. Assume also that the parachute accounts for essentially all the resistive force.

c) How much would the payload have to be reduced to cut the limiting velocity in half?

Explanation / Answer

MASS OF OBJECT = M DOWN WARD VELOCITY = Vo RESISTANCE OF ATMOSPHERE =F= F= -K*V

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