Question

A diver stands at the very end of a diving board before beginning a dive (see the figure). The deflection d of the board at a position s feet from the stationary end is given by d = cs2(5L − s) for 0 ≤ s ≤ L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physical properties of the board. Suppose the board is 20 feet long.
(a) If the deflection at the end of the board is 2 feet, find c.
(b) Show that the deflection is 1/2 ft somewhere between s = 9.3 and s = 9.4. (Round your answers to four decimal places.)

Answer 1

what is cs , c * s >

Answer 2

\[2=cs^2(5(20)-s)\]
\[c=\frac{ 2 }{ 100s^2-s^3 }\]

Answer 3

for part a i have s=20 d=2 l=20

Answer 4

i think i know where i messed up i did not multiply 20 by 5

Answer 5

c = 2 / ( s^2 (100-s) ) , but what is s?

Answer 6

ok that depends, now substitute that
d = [2/(s^2(100-s)) ] s^2 (100-S) ?

Answer 7

s=20

Answer 8

in part a

Answer 9

ok

Answer 10

c = .0000625

Answer 11

in part b d(9.3)= ? <0.5< ?=d(9.4)

Answer 12

yes,
d(.93) = .0000625 (9.3)^2 (100 - 9.3) = .4902

Answer 13

d(s) = .0000625 s^2 (100 - s)
d(.94 ) = .5003385

Answer 14

why did you make 9.3 .93?

Answer 15

typo

Answer 16

woops

Answer 17

ok

Answer 18

d(.93) = .0000625 (.93)^2 (100 - .93) = .4902