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Step 1Answer is mentioned belowStep 2The equation modelling the physical problem is,m(dv)/(dt)=mg-kv-(1)Here, k=4{:[mg=196N],[m=(196)/(9.8)=20kg]:}The ball is droped from height of 100m.:. equation (1) becomes{:[(dv)/(dt)=(mg-kv)/(m)=(196-4v.)/(20)],[=>(dv)/(196-4v)=(dt)/(20)],[(dv)/(4(49-v))=(dt)/(20)]:}Integrating this equation, we get{:[(-1)/(4)ln(49-v)=(1)/(20)t+c],[ln(49-v)=(-4)/(20)t-c_(1)],[49-v=e^(-(4)/(20)t-c_(1))],[49-v=c_(3)e^(-t//5)],[v=49-c_(3)e^(-t//5)]:}given initial velocity V=0 at t=0Step 3{:[=>0=49-c_(3)],[=>c_(3)=49],[:.v(t)=49(1-e^(-t//5))m//s]:}is the intant ... See the full answer