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18. 程式(a) and (b):
g = 9.81;
% Part a
v = 10;A = 35*(pi/180);
t_hit = (2/g)*v*sin(A);
t = [0:t_hit/1000:t_hit];
h = v*t*sin(A)-.5*g*t.^2;
[peak_height,i_peak] = max(h);
t_peak = i_peak*t_hit/1000;
peak_height
distance = v*t_hit*cos(A)
t_hit
% Part b
x=v*t*cos(A);
plot(x,h),xlabel(‘Distance (meters)’),ylabel(‘Height (meters)’)
圖 (b)
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程式(c)
g = 9.81;
v = 10;A = [20,30,45,60,70]*(pi/180);
t_hit = (2/g)*v*sin(A);
t = [0:max(t_hit)/1000:max(t_hit)]’;
sA = sin(A);
cA = cos(A);
r = 0.5*g*t.^2;
X = v*[t*cA(1),t*cA(2),t*cA(3),t*cA(4),t*cA(5)];
r = 0.5*g*t.^2;
R = [r,r,r,r,r];
Q = v*[t*sA(1),t*sA(2),t*sA(3),t*sA(4),t*sA(5)];
H = Q-R;
max_x = v*t_hit(3)*cA(3);
plot(X,H),axis([0 max_x 0 max(max(H))]),xlabel(‘Distance (m)’),...
ylabel(‘Height (m)’),gtext(‘20 deg’),gtext(‘30 deg’),...
gtext(‘45 deg’),gtext(‘60 deg’),gtext(‘70 deg’)
圖 (c)
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程式(d):
g = 9.81;A = 45*(pi/180);
v = [10:2:18];
t_hit = (2/g)*v*sin(A);
t = [0:max(t_hit)/1000:max(t_hit)]0;
r = 0.5*g*t.^2;
X = cos(A)*[t*v(1),t*v(2),t*v(3),t*v(4),t*v(5)];
R = [r,r,r,r,r];
Q = sin(A)*[t*v(1),t*v(2),t*v(3),t*v(4),t*v(5)];
H = Q-R;
plot(X,H),axis([0 max(max(X)) 0 max(max(H))]),xlabel(‘Distance (m)’),...
ylabel(‘Height (m)’),gtext(‘10 m/s’),gtext(‘12 m/s’),...
gtext(‘14 m/s’),gtext(‘16 m/s’),gtext(‘18 m/s’)
圖 (d)
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21.
Clear all;clc;
t = [0:8,10];
s = [0, 1210, 1866, 2301, 2564, 2724, 2881, 2879, 2915,
3010];
• plot(t, s,’*’,t, s,’--’), xlabel(‘Time (sec)’), ylabel(‘Speed
(rpm)’)
• 24. A與V 均為 r的次冪函數(power function)，因此可在loglog軸上為直線
• 程式(a)
• r = logspace(-1,2,300);
• V = (4/3)*pi*r.^3;
• A = 4*pi*r.^2;
• subplot(2,1,1)
• loglog(r,A),xlabel(‘Radius r (meters)’),ylabel(‘Area A
(meters^2)’)
• subplot(2,1,2)
• loglog(r,V), xlabel(‘Radius r (meters)’), ylabel(‘Volume
(meters^3)’)
程式(b):
A = logspace(0,4,300);
r = 0.5*sqrt(A/pi);
V = (1/(6*sqrt(pi)))*A.^(3/2);
subplot(2,1,1)
loglog(A,r),xlabel(‘Area A (meters^2)’),ylabel(‘Radius r
(meters)’)
• subplot(2,1,2)
• loglog(A,V),xlabel(‘Area A (meters^2)’),ylabel(‘Volume V
(meters^3)’)
• 圖示:
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