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28 May, 03:02

A hare and a tortoise compete in a race over a straight course 1.55 km long. The tortoise crawls at a speed of 0.100 m/s toward the finish line. The hare runs at a speed of 7.85 m/s toward the finish line for 1.240 km and then stops to tease the slow-moving tortoise as the tortoise eventually passes by. The hare waits for a while after the tortoise passes and then runs toward the finish line again at 7.85 m/s. Both the hare and the tortoise cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds.

Required:

How far is the tortoise from the finish line when the hare resumes the race?

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Answers (1)
  1. 28 May, 03:05
    0
    The tortoise is 3.95 m from the finish line when the hare resumes the race

    Explanation:

    Since, both the tortoise and the rabbit continue with the same uniform speed. Therefore, we will use the equation for constant speed, that is:

    s = vt

    t = s/v

    where,

    s = distance covered

    v = speed

    t = time taken

    Now, we consider the motion of tortoise:

    t₁ = s₁/v₁

    For hare:

    t₂ = s₂/v₂

    According to the given condition both hare and tortoise cross the finish line at same instant. Therefore, time for both must be equal.

    t₁ = t₂

    using values:

    s₁/v₁ = s₂/v₂

    where,

    s₁ = distance of tortoise from finish line when hare starts = ?

    v₁ = speed of tortoise = 0.1 m/s

    s₂ = distance of hare from finish line when he starts = 1.55 km - 1.24 km = 0.31 km = 310 m

    v₂ = speed of hare = 7.85 m/s

    Therefore,

    s₁ / (0.1 m/s) = (310 m) / (7.85 m/s)

    s₁ = (0.1 m/s) (39.5 s)

    s₁ = 3.95 m
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