A speedy tortoise can run at 0.13 m/s, and a
hare can run 16 times as fast. In a race, they
start at the same time, but the hare stops to
rest for 1.6 min, so the tortoise wins by a shell
(20 cm).
How long does the race take?
Answer in units of s.
Part 2
What is the length of the race?
Answer in units of m.
Help with Physics problem?
2015-09-01 5:06 am
回答 (2)
2015-09-01 5:24 am
✔ 最佳答案
Part 1 :Let y s be the time taken.
Then, time taking for the hare to run = (y - 1.6 × 60) s
Speed of the tortoise = 0.13 m/s
Speed of the hare = 0.13 × 16 m/s
0.13y - (0.13 × 16) × (y - 1.6 × 60) = 20/100
0.13y - 2.08 × (y - 96) = 0.2
0.13y - 2.08 y + 199.68 = 0.2
1.95y = 199.48
y = 102.3
Time taken = 102.3 s
Part 2 :
Length of the race
= 0.13 × 102.3 m
= 13.3 m
2015-09-01 6:59 am
(0.13*16) = 2.08m/sec.
(1.6m*60) = 96 secs.
20cm = 0.2m.
Effectively, the hare is starting (96*2.08) = 199.68 metres behind the start line, and running continuously.
The difference in their speeds = (2.08 - 0.13) = 1.95m/sec. This is the closure rate.
Time for hare to reach a point 0.2m. behind the hare = (199.68 - 0.2)/1.95 = 102.3 secs. This is the race time.
In 102.3 secs., the tortoise has run (102.3*0.13) = 13.3 metres, which was the race length.
(1.6m*60) = 96 secs.
20cm = 0.2m.
Effectively, the hare is starting (96*2.08) = 199.68 metres behind the start line, and running continuously.
The difference in their speeds = (2.08 - 0.13) = 1.95m/sec. This is the closure rate.
Time for hare to reach a point 0.2m. behind the hare = (199.68 - 0.2)/1.95 = 102.3 secs. This is the race time.
In 102.3 secs., the tortoise has run (102.3*0.13) = 13.3 metres, which was the race length.
收錄日期: 2021-05-02 11:13:53
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