Inserting the formulas you found for Xman(t) and Xbus(t) into the conditionXman(tcatch)=Xbus(tcatch) , you obtain the following-b+ct(catch) = 1/2 at^2( catch) or 1/2 at^2 (catch) - ct (catch) +b = 0Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man's speed (c) so that the equation above gives a solution for t catch that is a real positive number.Find Cmin the minimum value of c for which the man will catch the busExpress the minimum value for the man's speed in terms of a and b .

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moya1316 moya1316 · Answer 1 · 2020-11-30T10:32:37+01:00

Answer:

c > √(2ab)

Explanation:

In this exercise we are asked to find the condition for c in such a way that the results have been real

The given equation is

½ a t² - c t + b = 0

we can see that this is a quadratic equation whose solution is

t = [c ±√(c² - 4 (½ a) b)] / 2

for the results to be real, the square root must be real, so the radicand must be greater than zero

c² -2a b > 0

c > √(2ab)