Racing Speedy
Posted on | February 7, 2010 | Comments Off
Racing Speedy
physics homework help! a speedy tortoise can run at 0.14 m/s...?
a speedy tortoise can run at 0.14 m/s and a hare can run 18 times as fast. in a race, they start at the same time, but the hare stops to rest for 2.6 minutes, so the tortoise wins by a shell (20 cm). how long does the race take? (answer in units of seconds). What is the length of the race? (answer in units of meters).
Let:
t be the time for the tortoise to finish,
s1 be the distance covered by the tortoise,
s2 be the distance covered by the hare when the tortoise finishes.
distance = speed * time
s1 is also the length of the race.
For the tortoise:
s1 = 0.14t ...(1)
The hare stops for 2.6 min = 2.6 * 60 = 156 sec.
For the hare:
s2 = (18 * 0.14)(t - 156)
s2 = 2.52t - 393.12 ...(2)
s1 - s2 = 0.20 ...(3)
Substituting in (3) for s1 from (1) and s2 from (2):
0.14t - 2.52t + 393.12 = 0.20
2.38t = 392.92
t = 165.092 sec.
The tortoise has wins in 165.092 sec, but if the race ends when the hare finishes, its duration is:
165.092 + 0.20 / 2.52
= 165.171 sec.
To 3 sig. fig, the duration is 165 sec. either way.
s1 = 0.14t
= 0.14 * 165.092
= 23.1 m.
The distance is 23.1 m.
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