body of mass 6 kg is projected vertically upward with an initial velocity 39 met

Question

body of mass 6 kg is projected vertically upward with an initial velocity 39 meters per second (thus a negative velocity).

The gravitational constant is g=9.8m/s2 (NOT 9.81). The air resistance is equal to k|v| where k is a constant. Remember the equation mv?=mg?kv (friction for velocity upwards is increasing the downward speed, so -k v is still correct for upward motion)

Find a formula for the velocity at any time ( in terms of k ):
v(t)=

Find the terminal velocity: v=

Find the limit (might need L'Hospital's rule) of this velocity for a fixed time t0 as the air resistance coefficient k goes to 0. (Write t0 as t0 in your answer.)
v(t0)=

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