A lion and a lion tamer are enclosed within a circular cage. If they move at the same speed but are both restricted by the cage, can the lion catch the lion tamer? (Represent the cage by a circle, and the lion and lion tamer as two point masses within it.)
The following table shows an assumed starting position for the tame and for the lion, and follows them second by second until within 2 feet of one another, assuming a radius of 100 feet for the ring in which the tamer eventually runs and that both the lion and the tamer run at 15 feet per second.
In the specific case, it takes 624 seconds for the separation to close to 2 feet.
distance
from center
lion tamer separa- ------------
seconds x y x y tion tamer lion
0.0 -26.0 15.0 40.0 69.3 85.4 80.0 30.0
1.0 -14.4 24.5 51.6 78.8 85.4 94.2 28.4
2.0 -2.5 33.7 63.4 77.3 79.1 100.0 33.8
3.0 10.7 40.7 74.3 67.0 68.8 100.0 42.1
4.0 25.1 44.9 83.4 55.1 59.3 100.0 51.4
5.0 40.0 45.7 90.7 42.0 50.9 100.0 60.7
6.0 54.6 42.7 96.0 28.0 43.9 100.0 69.3
7.0 67.9 35.8 99.1 13.3 38.4 100.0 76.7
8.0 78.7 25.4 100.0 -1.6 34.4 100.0 82.7
9.0 86.3 12.5 98.6 -16.5 31.6 100.0 87.2
10.0 90.4 -1.9 95.0 -31.1 29.6 100.0 90.4
11.0 91.1 -16.8 89.3 -44.9 28.2 100.0 92.6
12.0 88.6 -31.6 81.6 -57.8 27.1 100.0 94.1
13.0 83.4 -45.6 72.1 -69.3 26.3 100.0 95.1
14.0 75.8 -58.5 60.9 -79.3 25.6 100.0 95.7
15.0 66.1 -69.9 48.3 -87.5 25.0 100.0 96.2
16.0 54.6 -79.6 34.7 -93.8 24.4 100.0 96.5
17.0 41.8 -87.3 20.3 -97.9 23.9 100.0 96.8
18.0 27.9 -92.9 5.5 -99.9 23.5 100.0 96.9
19.0 13.2 -96.2 -9.5 -99.5 23.0 100.0 97.1
20.0 -1.7 -97.2 -24.3 -97.0 22.6 100.0 97.2
21.0 -16.6 -95.9 -38.5 -92.3 22.2 100.0 97.3
22.0 -31.2 -92.3 -51.9 -85.5 21.8 100.0 97.5
23.0 -45.0 -86.5 -64.1 -76.8 21.4 100.0 97.5
24.0 -57.8 -78.7 -74.8 -66.3 21.1 100.0 97.6
25.0 -69.2 -69.0 -83.9 -54.4 20.7 100.0 97.7
26.0 -79.0 -57.7 -91.1 -41.3 20.4 100.0 97.8
27.0 -86.9 -45.0 -96.2 -27.2 20.0 100.0 97.9
28.0 -92.8 -31.2 -99.2 -12.5 19.7 100.0 97.9
29.0 -96.6 -16.7 -100.0 2.5 19.4 100.0 98.0
30.0 -98.1 -1.8 -98.5 17.4 19.1 100.0 98.1
31.0 -97.2 13.2 -94.8 31.9 18.9 100.0 98.1
32.0 -94.2 27.9 -88.9 45.7 18.6 100.0 98.2
33.0 -88.9 41.9 -81.1 58.5 18.3 100.0 98.2
34.0 -81.5 54.9 -71.5 69.9 18.0 100.0 98.3
35.0 -72.3 66.7 -60.2 79.8 17.8 100.0 98.3
36.0 -61.3 77.0 -47.6 87.9 17.6 100.0 98.4
37.0 -48.9 85.4 -33.9 94.1 17.3 100.0 98.4
38.0 -35.4 91.9 -19.5 98.1 17.1 100.0 98.5
39.0 -21.1 96.2 -4.6 99.9 16.9 100.0 98.5
40.0 -6.2 98.4 10.4 99.5 16.6 100.0 98.6
41.0 8.7 98.2 25.1 96.8 16.4 100.0 98.6
42.0 23.5 95.8 39.3 92.0 16.2 100.0 98.6
43.0 37.8 91.2 52.6 85.1 16.0 100.0 98.7
44.0 51.2 84.4 64.7 76.2 15.8 100.0 98.7
45.0 63.4 75.7 75.4 65.7 15.6 100.0 98.7
46.0 74.1 65.3 84.3 53.7 15.4 100.0 98.8
47.0 83.2 53.3 91.4 40.5 15.3 100.0 98.8
48.0 90.3 40.2 96.5 26.4 15.1 100.0 98.8
49.0 95.4 26.1 99.3 11.7 14.9 100.0 98.9
50.0 98.2 11.3 99.9 -3.3 14.7 100.0 98.9
51.0 98.8 -3.6 98.3 -18.2 14.6 100.0 98.9
52.0 97.2 -18.5 94.5 -32.7 14.4 100.0 98.9
53.0 93.3 -33.0 88.6 -46.4 14.3 100.0 99.0
54.0 87.3 -46.7 80.6 -59.2 14.1 100.0 99.0
55.0 79.2 -59.4 70.9 -70.5 13.9 100.0 99.0
56.0 69.4 -70.7 59.5 -80.3 13.8 100.0 99.0
57.0 57.9 -80.3 46.9 -88.3 13.7 100.0 99.0
58.0 45.2 -88.2 33.1 -94.3 13.5 100.0 99.1
59.0 31.4 -94.0 18.7 -98.2 13.4 100.0 99.1
60.0 16.8 -97.7 3.8 -99.9 13.2 100.0 99.1
61.0 1.9 -99.1 -11.2 -99.4 13.1 100.0 99.1
62.0 -13.1 -98.3 -25.9 -96.6 13.0 100.0 99.1
63.0 -27.7 -95.2 -40.1 -91.6 12.8 100.0 99.2
64.0 -41.8 -90.0 -53.3 -84.6 12.7 100.0 99.2
65.0 -54.8 -82.7 -65.3 -75.7 12.6 100.0 99.2
66.0 -66.7 -73.5 -75.9 -65.1 12.5 100.0 99.2
67.0 -77.0 -62.6 -84.8 -53.0 12.4 100.0 99.2
68.0 -85.6 -50.3 -91.8 -39.7 12.2 100.0 99.2
69.0 -92.2 -36.8 -96.7 -25.6 12.1 100.0 99.3
70.0 -96.7 -22.5 -99.4 -10.8 12.0 100.0 99.3
71.0 -99.0 -7.7 -99.9 4.1 11.9 100.0 99.3
72.0 -99.0 7.2 -98.2 19.0 11.8 100.0 99.3
73.0 -96.8 22.1 -94.2 33.5 11.7 100.0 99.3
74.0 -92.4 36.4 -88.2 47.2 11.6 100.0 99.3
75.0 -85.9 49.9 -80.1 59.8 11.5 100.0 99.3
76.0 -77.4 62.2 -70.3 71.1 11.4 100.0 99.3
77.0 -67.2 73.2 -58.9 80.8 11.3 100.0 99.4
78.0 -55.4 82.5 -46.1 88.7 11.2 100.0 99.4
79.0 -42.4 89.9 -32.4 94.6 11.1 100.0 99.4
80.0 -28.4 95.2 -17.9 98.4 11.0 100.0 99.4
81.0 -13.8 98.4 -2.9 100.0 10.9 100.0 99.4
82.0 1.2 99.4 12.0 99.3 10.8 100.0 99.4
83.0 16.1 98.1 26.7 96.4 10.7 100.0 99.4
84.0 30.7 94.6 40.8 91.3 10.7 100.0 99.4
85.0 44.6 88.9 54.0 84.2 10.6 100.0 99.4
86.0 57.4 81.2 66.0 75.1 10.5 100.0 99.4
87.0 69.0 71.7 76.5 64.4 10.4 100.0 99.5
88.0 79.0 60.5 85.2 52.3 10.3 100.0 99.5
89.0 87.2 47.9 92.1 39.0 10.2 100.0 99.5
90.0 93.4 34.3 96.9 24.8 10.2 100.0 99.5
91.0 97.5 19.9 99.5 10.0 10.1 100.0 99.5
92.0 99.4 5.0 99.9 -5.0 10.0 100.0 99.5
93.0 99.0 -10.0 98.0 -19.8 9.9 100.0 99.5
94.0 96.4 -24.7 93.9 -34.3 9.9 100.0 99.5
95.0 91.6 -38.9 87.8 -47.9 9.8 100.0 99.5
96.0 84.7 -52.2 79.6 -60.5 9.7 100.0 99.5
97.0 75.9 -64.4 69.7 -71.7 9.6 100.0 99.5
98.0 65.4 -75.0 58.2 -81.3 9.6 100.0 99.5
99.0 53.4 -84.0 45.4 -89.1 9.5 100.0 99.5
100.0 40.2 -91.1 31.6 -94.9 9.4 100.0 99.6
101.0 26.1 -96.1 17.0 -98.5 9.4 100.0 99.6
102.0 11.3 -98.9 2.1 -100.0 9.3 100.0 99.6
103.0 -3.6 -99.5 -12.9 -99.2 9.2 100.0 99.6
104.0 -18.5 -97.8 -27.5 -96.1 9.2 100.0 99.6
105.0 -33.0 -94.0 -41.6 -90.9 9.1 100.0 99.6
106.0 -46.7 -87.9 -54.7 -83.7 9.0 100.0 99.6
107.0 -59.4 -79.9 -66.6 -74.6 9.0 100.0 99.6
108.0 -70.7 -70.1 -77.0 -63.8 8.9 100.0 99.6
109.0 -80.4 -58.7 -85.7 -51.6 8.9 100.0 99.6
110.0 -88.4 -46.0 -92.4 -38.2 8.8 100.0 99.6
111.0 -94.3 -32.2 -97.1 -24.0 8.7 100.0 99.6
112.0 -98.0 -17.7 -99.6 -9.2 8.7 100.0 99.6
113.0 -99.6 -2.8 -99.8 5.8 8.6 100.0 99.6
114.0 -98.9 12.1 -97.8 20.7 8.6 100.0 99.6
115.0 -96.0 26.8 -93.7 35.0 8.5 100.0 99.6
116.0 -90.8 40.9 -87.4 48.7 8.5 100.0 99.6
117.0 -83.7 54.1 -79.1 61.2 8.4 100.0 99.6
118.0 -74.6 66.0 -69.1 72.3 8.4 100.0 99.6
119.0 -63.9 76.5 -57.5 81.8 8.3 100.0 99.7
120.0 -51.7 85.2 -44.6 89.5 8.3 100.0 99.7
121.0 -38.3 92.0 -30.8 95.2 8.2 100.0 99.7
122.0 -24.1 96.7 -16.2 98.7 8.2 100.0 99.7
123.0 -9.3 99.2 -1.3 100.0 8.1 100.0 99.7
124.0 5.6 99.5 13.7 99.1 8.1 100.0 99.7
125.0 20.5 97.5 28.3 95.9 8.0 100.0 99.7
126.0 34.9 93.4 42.3 90.6 8.0 100.0 99.7
127.0 48.5 87.1 55.4 83.2 7.9 100.0 99.7
128.0 61.0 78.8 67.2 74.0 7.9 100.0 99.7
129.0 72.1 68.8 77.5 63.2 7.8 100.0 99.7
130.0 81.6 57.2 86.1 50.9 7.8 100.0 99.7
131.0 89.3 44.3 92.7 37.4 7.7 100.0 99.7
132.0 94.9 30.5 97.3 23.1 7.7 100.0 99.7
133.0 98.4 15.9 99.7 8.3 7.6 100.0 99.7
134.0 99.7 0.9 99.8 -6.6 7.6 100.0 99.7
135.0 98.7 -14.0 97.7 -21.5 7.5 100.0 99.7
136.0 95.5 -28.6 93.4 -35.8 7.5 100.0 99.7
137.0 90.1 -42.6 87.0 -49.4 7.5 100.0 99.7
138.0 82.7 -55.7 78.6 -61.8 7.4 100.0 99.7
139.0 73.5 -67.4 68.5 -72.9 7.4 100.0 99.7
140.0 62.5 -77.7 56.8 -82.3 7.3 100.0 99.7
141.0 50.2 -86.2 43.9 -89.9 7.3 100.0 99.7
142.0 36.7 -92.7 30.0 -95.4 7.3 100.0 99.7
143.0 22.4 -97.2 15.4 -98.8 7.2 100.0 99.7
144.0 7.6 -99.5 0.4 -100.0 7.2 100.0 99.7
145.0 -7.4 -99.5 -14.5 -98.9 7.1 100.0 99.7
146.0 -22.2 -97.2 -29.1 -95.7 7.1 100.0 99.7
147.0 -36.5 -92.8 -43.1 -90.2 7.1 100.0 99.8
148.0 -50.0 -86.3 -56.1 -82.8 7.0 100.0 99.8
149.0 -62.4 -77.8 -67.8 -73.5 7.0 100.0 99.8
150.0 -73.3 -67.6 -78.1 -62.5 7.0 100.0 99.8
151.0 -82.7 -55.9 -86.5 -50.1 6.9 100.0 99.8
152.0 -90.1 -42.9 -93.0 -36.6 6.9 100.0 99.8
153.0 -95.5 -28.9 -97.5 -22.3 6.8 100.0 99.8
154.0 -98.7 -14.3 -99.7 -7.5 6.8 100.0 99.8
155.0 -99.8 0.7 -99.7 7.5 6.8 100.0 99.8
156.0 -98.5 15.6 -97.5 22.3 6.7 100.0 99.8
157.0 -95.1 30.2 -93.1 36.6 6.7 100.0 99.8
158.0 -89.5 44.1 -86.5 50.1 6.7 100.0 99.8
159.0 -81.9 57.0 -78.1 62.5 6.6 100.0 99.8
160.0 -72.4 68.6 -67.9 73.4 6.6 100.0 99.8
161.0 -61.3 78.7 -56.1 82.8 6.6 100.0 99.8
162.0 -48.8 87.0 -43.1 90.2 6.5 100.0 99.8
163.0 -35.3 93.4 -29.2 95.7 6.5 100.0 99.8
164.0 -20.9 97.6 -14.6 98.9 6.5 100.0 99.8
165.0 -6.0 99.6 0.4 100.0 6.4 100.0 99.8
166.0 8.9 99.4 15.3 98.8 6.4 100.0 99.8
167.0 23.7 96.9 29.9 95.4 6.4 100.0 99.8
168.0 38.0 92.3 43.9 89.9 6.4 100.0 99.8
169.0 51.4 85.6 56.8 82.3 6.3 100.0 99.8
170.0 63.6 76.9 68.5 72.9 6.3 100.0 99.8
171.0 74.4 66.5 78.6 61.9 6.3 100.0 99.8
172.0 83.5 54.6 86.9 49.4 6.2 100.0 99.8
173.0 90.8 41.5 93.3 35.9 6.2 100.0 99.8
174.0 96.0 27.5 97.7 21.5 6.2 100.0 99.8
175.0 99.0 12.8 99.8 6.7 6.1 100.0 99.8
176.0 99.8 -2.2 99.7 -8.3 6.1 100.0 99.8
177.0 98.3 -17.1 97.3 -23.1 6.1 100.0 99.8
178.0 94.7 -31.6 92.8 -37.4 6.1 100.0 99.8
179.0 88.9 -45.5 86.1 -50.8 6.0 100.0 99.8
180.0 81.1 -58.2 77.6 -63.1 6.0 100.0 99.8
181.0 71.4 -69.7 67.3 -74.0 6.0 100.0 99.8
182.0 60.2 -79.6 55.4 -83.2 6.0 100.0 99.8
183.0 47.6 -87.7 42.4 -90.6 5.9 100.0 99.8
184.0 33.9 -93.9 28.4 -95.9 5.9 100.0 99.8
185.0 19.5 -97.9 13.7 -99.1 5.9 100.0 99.8
186.0 4.6 -99.7 -1.2 -100.0 5.8 100.0 99.8
187.0 -10.4 -99.3 -16.2 -98.7 5.8 100.0 99.8
188.0 -25.1 -96.6 -30.7 -95.2 5.8 100.0 99.8
189.0 -39.3 -91.8 -44.6 -89.5 5.8 100.0 99.8
190.0 -52.6 -84.9 -57.5 -81.8 5.7 100.0 99.8
191.0 -64.7 -76.0 -69.1 -72.3 5.7 100.0 99.8
192.0 -75.4 -65.5 -79.1 -61.2 5.7 100.0 99.8
193.0 -84.3 -53.5 -87.3 -48.7 5.7 100.0 99.8
194.0 -91.4 -40.3 -93.6 -35.1 5.6 100.0 99.8
195.0 -96.4 -26.1 -97.8 -20.7 5.6 100.0 99.8
196.0 -99.2 -11.4 -99.8 -5.8 5.6 100.0 99.8
197.0 -99.8 3.6 -99.6 9.1 5.6 100.0 99.8
198.0 -98.1 18.5 -97.1 23.9 5.6 100.0 99.8
199.0 -94.3 32.9 -92.4 38.2 5.5 100.0 99.8
200.0 -88.3 46.7 -85.7 51.5 5.5 100.0 99.9
201.0 -80.3 59.4 -77.0 63.8 5.5 100.0 99.9
202.0 -70.5 70.7 -66.6 74.6 5.5 100.0 99.9
203.0 -59.1 80.5 -54.7 83.7 5.4 100.0 99.9
204.0 -46.4 88.4 -41.6 90.9 5.4 100.0 99.9
205.0 -32.7 94.4 -27.6 96.1 5.4 100.0 99.9
206.0 -18.2 98.2 -12.9 99.2 5.4 100.0 99.9
207.0 -3.3 99.8 2.1 100.0 5.4 100.0 99.9
208.0 11.7 99.2 17.0 98.5 5.3 100.0 99.9
209.0 26.4 96.3 31.5 94.9 5.3 100.0 99.9
210.0 40.5 91.3 45.3 89.1 5.3 100.0 99.9
211.0 53.7 84.2 58.2 81.4 5.3 100.0 99.9
212.0 65.7 75.2 69.7 71.7 5.2 100.0 99.9
213.0 76.2 64.5 79.6 60.5 5.2 100.0 99.9
214.0 85.0 52.4 87.8 48.0 5.2 100.0 99.9
215.0 91.9 39.1 93.9 34.3 5.2 100.0 99.9
216.0 96.7 24.9 98.0 19.9 5.2 100.0 99.9
217.0 99.4 10.1 99.9 5.0 5.1 100.0 99.9
218.0 99.8 -4.8 99.5 -10.0 5.1 100.0 99.9
219.0 97.9 -19.7 96.9 -24.7 5.1 100.0 99.9
220.0 93.9 -34.1 92.1 -38.9 5.1 100.0 99.9
221.0 87.7 -47.8 85.3 -52.3 5.1 100.0 99.9
222.0 79.6 -60.4 76.5 -64.4 5.0 100.0 99.9
223.0 69.6 -71.6 66.0 -75.1 5.0 100.0 99.9
224.0 58.1 -81.2 54.0 -84.1 5.0 100.0 99.9
225.0 45.3 -89.0 40.9 -91.3 5.0 100.0 99.9
226.0 31.5 -94.8 26.8 -96.4 5.0 100.0 99.9
227.0 17.0 -98.4 12.1 -99.3 5.0 100.0 99.9
228.0 2.0 -99.9 -2.9 -100.0 4.9 100.0 99.9
229.0 -12.9 -99.0 -17.8 -98.4 4.9 100.0 99.9
230.0 -27.6 -96.0 -32.3 -94.6 4.9 100.0 99.9
231.0 -41.7 -90.8 -46.1 -88.7 4.9 100.0 99.9
232.0 -54.8 -83.5 -58.8 -80.9 4.9 100.0 99.9
233.0 -66.6 -74.4 -70.3 -71.2 4.8 100.0 99.9
234.0 -77.0 -63.6 -80.1 -59.9 4.8 100.0 99.9
235.0 -85.7 -51.4 -88.1 -47.2 4.8 100.0 99.9
236.0 -92.4 -38.0 -94.2 -33.5 4.8 100.0 99.9
237.0 -97.0 -23.7 -98.2 -19.1 4.8 100.0 99.9
238.0 -99.5 -8.9 -99.9 -4.2 4.8 100.0 99.9
239.0 -99.7 6.1 -99.4 10.8 4.7 100.0 99.9
240.0 -97.7 20.9 -96.7 25.5 4.7 100.0 99.9
241.0 -93.5 35.3 -91.8 39.7 4.7 100.0 99.9
242.0 -87.1 48.9 -84.8 53.0 4.7 100.0 99.9
243.0 -78.8 61.4 -76.0 65.0 4.7 100.0 99.9
244.0 -68.8 72.5 -65.4 75.7 4.7 100.0 99.9
245.0 -57.2 81.9 -53.3 84.6 4.6 100.0 99.9
246.0 -44.3 89.6 -40.1 91.6 4.6 100.0 99.9
247.0 -30.4 95.2 -26.0 96.6 4.6 100.0 99.9
248.0 -15.8 98.6 -11.2 99.4 4.6 100.0 99.9
249.0 -0.8 99.9 3.7 99.9 4.6 100.0 99.9
250.0 14.1 98.9 18.6 98.3 4.6 100.0 99.9
251.0 28.7 95.7 33.1 94.4 4.5 100.0 99.9
252.0 42.7 90.3 46.8 88.4 4.5 100.0 99.9
253.0 55.8 82.9 59.5 80.4 4.5 100.0 99.9
254.0 67.5 73.6 70.8 70.6 4.5 100.0 99.9
255.0 77.8 62.7 80.6 59.2 4.5 100.0 99.9
256.0 86.3 50.4 88.5 46.5 4.5 100.0 99.9
257.0 92.8 36.9 94.5 32.7 4.5 100.0 99.9
258.0 97.3 22.6 98.3 18.3 4.4 100.0 99.9
259.0 99.6 7.8 99.9 3.4 4.4 100.0 99.9
260.0 99.6 -7.2 99.3 -11.6 4.4 100.0 99.9
261.0 97.4 -22.0 96.5 -26.3 4.4 100.0 99.9
262.0 93.1 -36.4 91.5 -40.5 4.4 100.0 99.9
263.0 86.6 -49.9 84.4 -53.7 4.4 100.0 99.9
264.0 78.1 -62.3 75.4 -65.7 4.4 100.0 99.9
265.0 67.9 -73.3 64.8 -76.2 4.3 100.0 99.9
266.0 56.2 -82.6 52.6 -85.0 4.3 100.0 99.9
267.0 43.2 -90.1 39.3 -91.9 4.3 100.0 99.9
268.0 29.3 -95.5 25.2 -96.8 4.3 100.0 99.9
269.0 14.7 -98.8 10.4 -99.5 4.3 100.0 99.9
270.0 -0.3 -99.9 -4.6 -99.9 4.3 100.0 99.9
271.0 -15.2 -98.7 -19.4 -98.1 4.3 100.0 99.9
272.0 -29.8 -95.4 -33.9 -94.1 4.2 100.0 99.9
273.0 -43.8 -89.8 -47.6 -88.0 4.2 100.0 99.9
274.0 -56.7 -82.3 -60.2 -79.9 4.2 100.0 99.9
275.0 -68.4 -72.9 -71.4 -70.0 4.2 100.0 99.9
276.0 -78.5 -61.8 -81.1 -58.5 4.2 100.0 99.9
277.0 -86.9 -49.4 -88.9 -45.8 4.2 100.0 99.9
278.0 -93.3 -35.8 -94.8 -32.0 4.2 100.0 99.9
279.0 -97.6 -21.5 -98.5 -17.4 4.2 100.0 99.9
280.0 -99.7 -6.7 -100.0 -2.5 4.1 100.0 99.9
281.0 -99.6 8.3 -99.2 12.4 4.1 100.0 99.9
282.0 -97.2 23.1 -96.3 27.1 4.1 100.0 99.9
283.0 -92.7 37.4 -91.1 41.2 4.1 100.0 99.9
284.0 -86.0 50.8 -83.9 54.4 4.1 100.0 99.9
285.0 -77.4 63.1 -74.9 66.3 4.1 100.0 99.9
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|
Posted by Charlie
on 2013-06-11 13:42:06 |