L3-013 非常弹的球 (30 分)
设掷出的角度为θ
m
=
w
100
m = \frac{w}{100}
m=100w?
E
=
m
v
2
2
E=\frac{mv^2}{2}
E=2mv2?
v
2
=
2
E
m
v^2=\frac{2E}{m}
v2=m2E?
V
x
=
2
E
?
100
w
?
c
o
s
θ
V_x=\sqrt{\frac{2E*100}{w}}*cosθ
Vx?=w2E?100?
??cosθ
V
y
=
2
E
?
100
w
?
s
i
n
θ
V_y=\sqrt{\frac{2E*100}{w}}*sinθ
Vy?=w2E?100?
??sinθ
t
=
2
V
y
g
t=\frac{2V_y}{g}
t=g2Vy??
S
=
2
V
x
V
y
g
=
4
E
?
100
w
s
i
n
θ
c
o
s
θ
=
2
E
?
100
w
g
s
i
n
2
θ
S=\frac{2V_xV_y}g =\frac{4E*100}{w}sinθcosθ =\frac{2E*100}{wg}sin2θ
S=g2Vx?Vy??=w4E?100?sinθcosθ=wg2E?100?sin2θ
当θ=45°时S最大
#include <iostream>
#include <iomanip>
using namespace std;
int w, p;
double v, s;
int main()
{
cin >> w >> p;
v = 2.0 * 1000 * 100 / w;
while (v > 0.00001)
{
s += v / 9.8;
v *= (100 - p) * 0.01;
}
cout << setprecision(3) << fixed << s << endl;
return 0;
}
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