Do I keep the initial value constant in or take it out? Please help and write your answer on paper. Thank you!

7. Let u ft per sec be the downward speed of a falling body. Gravity will continue to increase the velocity endlessly. However, air friction will coun- teract gravity. Assume that the friction force is proportional to the speed e. Then the equation of motion takes the form, du (t) = mg - kv(t) where m lbs is its mass and g is the gravitational constant. Determine the terminal velocity of the body when m = 150 lbs and k = 60 lbs/sec. Answer: 80 ft/sec. Suppose the body begins its fall at height H ft. How far does the body fall before it reaches 90% of its terminal velocity? Answer: 280 ft. M of du ( + ) = my - kv (+ ) = > m V (t ) + K V (t ) = mg = ODE Homogenious solution! U. ( + ) = cent = > mce"+ Kcelt = 0 - k + Cent ( ma + k ) - O Vn(t ) = C(x)e 1 = -K micexbent - c( x ) . = mg mc lx ) emt - kc ( x )ent ( ( x ) = gent => c( x ) = glem of - g. k ent + c V ( + ) =19M e + ce m = > V ( + ) = 19m e e' it K K V ( D ) = I + C = 0 gm - gm K C = -gm K If I leave c out I get right answer . if I keep it in , I get rong