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## Homework Statement

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.

## Homework Equations

None.

## 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.