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
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