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Problem 1
(70 points)
The most
powerful
cannon o ever
seeaction
was
"Schwer
Gustav"
(Heavy
Gustav) which was used by
'
Germany
n the siegeof Sevastapol
44o
N latitude) Ukraine,
n June
of
1942.
The
projectiles
were
80
cm
(-31.5")
in diameter,and had masses p to
7100
kg. One
particular
projectile
(which
we will analyze
here)(see iagrambelow) had a massof
4800
kg
(-5.3
tons), amuzzle
velocity
(vp)
of 820 m/s, and
was
reported o
have
a
range
of
48 km
(on
impact t reportedly
produced
a crater
30 ft deepand 30+ ft across).
For the
purpose
of
this analysis
suppose hatSchwer
Gustav
was ocatedat 44o
N
latitude
and was firing
(aimed)
due North, with a barrel
nclination
of 30oup
from the horizontal. You
may assume hat the
terrain
is
absolutely
lat.
You
may
also
consider
standard
ravity (9.S1
m/s2)as
being valid at this
location, and
you
DO NOT NEED TO CONSIDER TFIE VARTATION IN
GRAVITY WITH
TFIE
ALTITUDE OF THE
PROJECTILE
(i.e.
treat
gravity
as constant
n
this
problem).
You may also assume
that
you
can neglectair resistance.
Youwill have o
make
someother
"EngineeringAssumptions/Approximations"
tere
(e.g.
what terms
you
can neglect and what
you
should keep).
Some
are more acceptable han others. Please cleorly state what
your
assumptions
are.
Neglecting the spin of the earthand using standard
ravity
of
9:9.81
[m/s2]
i.e.
using what
you
learned
in basicdynamics):
A) What is the
time of flight for
the
projectile?
t'
B) What are
he expected
x,y)
coordinates elative o the
cannonof where his
projectile
will
land?
(using
tl-du. east,
1t
due
north, and
zt-vertical).
{
Now
considering he
rotation
of the earth(butneglecting
he change
n
gravity
with altitude):
C)
Produce he scalar
hree equations
of motion
(i.e.
Newton's
2no aw of Motion)(one associated ith
eachof
the i
,
,k
directions)
numerical
alue)
-
';
n
From the k
equation,
what
is the actually apparent
acceleration f
gravity,
Z
(numerical
value)?
)
E)
F)
G)
F)
A
From the
j
equation,what is the apparent acceleration,
(numerical
value)?
What
is finaly locationof the
mpact?
'r
From
the i equation,
what s
your
estimate f the apparent
acceleration, ?
(value)'
,
is final x locationof the
mpact?
15 pts)
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