急 ! F5 變分計法 7q02

12.
(a)
R : resistance
v : speed

R ∝ v³
Then, R = kv³
where k is constant.

When v = vo, R = Ro :
Ro = kvo³

When v = 2vo :
R = k(2vo)³
R = 8kv³
R = 8Ro

New resistance : Original resistance
= 8Ro : Ro
= 8 : 1

(b)
When v = vo(1 + 10%) :
R = k[vo(1 + 10%)]³
R = 1.331kvo³
R = 1.331Ro

% increase in resistance
= [(1.331Ro - Ro)/Ro] x 100%
= 33.1%


13.
W ∝ 1/d²
Then, W = k/d²
where k is constant.

When d = (6400 + 4200), W = 22 :
22 = k/(6400 + 4200)²
k = 22*(10600)²

Hence, W = 22*(10600)²/d²

When d = (6400 + 1500) :
W = 22*(10600)²/(6400 + 1500)²
W = 39.6

When the space shuttle is the nearest to the centre of the Earth,
the weight of the spaceman = 39.6 kg


14.
(a)
(To read the graph, read x-axis as "N" and y-axis as "E".)
(For example, a straight line y = x + 1 should read E = N + 1.)

E is partly constant C and partly varies directly as N.
Then, E = C + kN
where C and k are constant.

When N = 0, E = C
From the graph : When N = 0, E = 600

Then C = 600

(b)
Slope of the graph
= (1000 - 600)/(40 - 0)
= 10

vertical intercept = 600

(Slope-intercept form of a st. line : y = mx + c)
Equation of the graph (slope-intercept form) :
E = 10N + 600
E = 600 + 10N

(c)
E = 600 + 10N

When N = 50 :
E = 600 + 10(50)
E = 1100

Amount that each player pays
= $1100/50
= $22