1. The problem statement, all variables and given/known data A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. Air resistance is proportional to speed, with k=1/128 lb-s/ft. Find the maximum height attained by the stone. 2. Relevant equations None. 3. The attempt at a solution Here's my work: mg+kv=m(dv/dt) (1/2)(-32)-(1/128)v=(1/2)(dv/dt) (dv/dt)+(1/64)v=-32 integrating factor method: e^(t/64) (e^(t/64))v=-2048e^(t/64)+C v=-2048+Ce^(-t/64) v(0)=32 C=2080 v=-2048+2080e^(-t/64) v(t)=h'(t) h'(t)=-2048+2080e^(-t/64) integrate h'(t), h(t)=-2048t-133120e^(-t/64)+C h(0)=5 C=133125 h(t)=-2048t-133120e^(-t/64)+133125 v(t)=0 when t=0.992268 h(0.992268)=20.8353 But the answer in the book says 17.10 ft. What's wrong? Is my answer correct? If not, then please correct me.