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NAMtr:
Suppose that you are on top of a 50 meter tall building and you toss a 2 kg ball upwards
with a speed of 40 m/sec. Assume that there is a resistance force whose magnitude is 4 times
the speed of the ball. How long will it take for the ball to reach its maximum height?
Start with F : ffra to determine the differential equation for u. Recall that it's easier to
write ma : F : Fs + F, and then replace " bv
#.Write the IVP for o in the box.
( Tql = - r u * - e /
IVP:
- - ) * = - 7 -J * v rh'
^t
^?,F- 2 t/
::
: fo
, 0r;(o)
Now solve folu and answer the question. Show your work.
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l_ f ,v-lv
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: [^r
= t+c
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fvLre
V=o'
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=-tf
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= e e
t
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A
L(0 = -{,f 'l- C
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V
-t't
- r . 7+ l t f e
pts)2. Define,Rto be the regionwith boundariesA: 12, the g axis,and the line a:4.
a) SketchR
(zr{)
b) Find the volume (to two decimal places) of the solid obtained by revolving ft about the
y axis.
Zrrr")1'L
{l--t
V /cx't)
L
/. rr u" b\
r."
t ' v
t
r l' f i
P - v f . -- \
dl
\flv
U
Jo
*Ar
- * t u l \ = vrT
-"?
'Lu
=
0
2s,{3
c) Find the volume (to two decimal places) of the solid obtained by revolving R about the
line g : 6.
a
I
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