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25% part (c) assume that d is the distance the cheetah is away from the gazelle when it reaches full speed. Derive an expression in terms of the variables d, vcmax and vg for the time, tc, it takes the cheetah to catch the gazelle.

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maximum speed of cheetah is


v_1 = v_(max)

speed of gazelle is given as


v_2 = v_(g)

Now the relative speed of Cheetah with respect to Gazelle


v_(12) = v_1 - v_2


v_(12) = v_(max) - v_g

now the relative distance between Cheetah and Gazelle is given initially as "d"

now the time taken by Cheetah to catch the Gazelle is given as


d = v_(12)* t

so by rearranging the terms we can say


t = (d)/(v_(12))


t = (d)/(v_(max) - v_g)

so above is the relation between all given variable

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