A Thomson’s gazelle can run at very high speeds, but its acceleration is relatively modest. A reasonable model for the sprint of a gazelle a

Question

A Thomson’s gazelle can run at very high speeds, but its acceleration is relatively modest. A reasonable model for the sprint of a gazelle assumes an acceleration of 4.2m/s2 for 6.5s , after which the gazelle CONTINUES at a steady speed.

a. What is the gazelles top speed?
b. A human would win a very short race with a gazelle. The best time for a 30 m sprint for a human runner is 3.6 s. How much time would the gazelle take for a 30 m race?

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Acacia 6 months 2021-08-02T07:27:57+00:00 1 Answers 65 views 0

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    2021-08-02T07:29:51+00:00

    Answer:

    The correct answer will be:

    (a) 27.3 m/s

    (b) 3.8 s

    Explanation:

    According to the question:

    Acceleration,

    a= 4.2 \ m/s^2

    Time,

    t = 6.5 \ s

    (a)

    The gazelles top speed will be:

    ⇒  V_{max} = at

                 =4.2\times 6.5

                 =27.3 \ m/s

    or,

                 = 27 \ m/s

    (b)

    As we know,

    s = 30 m

    Now,

    ⇒  s = \frac{1}{2} at^2

    or,

    ⇒  t=\sqrt{\frac{2s}{a} }

    On putting the given values, we get

           =\sqrt{\frac{2\times 30}{4.2} }

           =\sqrt{\frac{60}{4.2} }

           =3.78 \ s

    or,

           =3.8 \ s

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