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Math10
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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.