If a diver of mass m stands at the end of a diving board with length L and linear density ρ , then the board takes on the shape of a curve y = f ( x ) , where E I y ′ ′ = m g ( L − x ) + 1 2 ρ g ( L − x ) 2 E and I are positive constants that depend on the material of the board and g ( < 0 ) is the acceleration due to gravity. (a) Find an expression for the shape of the curve. (b) Use f ( L ) to estimate the distance below the horizontal at the end of the board.
If a diver of mass m stands at the end of a diving board with length L and linear density ρ , then the board takes on the shape of a curve y = f ( x ) , where E I y ′ ′ = m g ( L − x ) + 1 2 ρ g ( L − x ) 2 E and I are positive constants that depend on the material of the board and g ( < 0 ) is the acceleration due to gravity. (a) Find an expression for the shape of the curve. (b) Use f ( L ) to estimate the distance below the horizontal at the end of the board.
Solution Summary: The author explains how to find a description of the curve's shape using the graphic calculator.
If a diver of mass
m
stands at the end of a diving board with length
L
and linear density
ρ
, then the board takes on the shape of a curve
y
=
f
(
x
)
, where
E
I
y
′
′
=
m
g
(
L
−
x
)
+
1
2
ρ
g
(
L
−
x
)
2
E
and
I
are positive constants that depend on the material of the board and
g
(
<
0
)
is the acceleration due to gravity.
(a) Find an expression for the shape of the curve.
(b) Use
f
(
L
)
to estimate the distance below the horizontal at the end of the board.
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