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Putnam
Putnam 1939
A6
A6
Part of
Putnam 1939
Problems
(1)
Putnam 1939 A6
Source:
8/20/2021
Do either
(
1
)
(1)
(
1
)
or
(
2
)
(2)
(
2
)
:
(
1
)
(1)
(
1
)
A circle radius
r
r
r
rolls around the inside of a circle radius
3
r
,
3r,
3
r
,
so that a point on its circumference traces out a curvilinear triangle. Find the area inside this figure.
(
2
)
(2)
(
2
)
A frictionless shell is fired from the ground with speed
v
v
v
at an unknown angle to the vertical. It hits a plane at a height
h
.
h.
h
.
Show that the gun must be sited within a radius
v
g
(
v
2
−
2
g
h
)
1
2
\frac{v}{g} (v^2 - 2gh)^{\frac{1}{2}}
g
v
(
v
2
−
2
g
h
)
2
1
of the point directly below the point of impact.
Putnam