Inserting the formulas you found for Xman(t) and Xbus(t) into the conditionXman(
ID: 2165934 • Letter: I
Question
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 = 0
Intuitively, 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 bus
Express the minimum value for the man's speed in terms of a and b .
Explanation / Answer
1/2*a*t^2 - ct +b = 0 For solution to exist det >0 c^2 - 4*b*1/2*a >= c^2 - 2ab > 0 Minimum of c = sqrt(2ab)