You did so well on the first problem. Six Flags decided to promote you to work o

Question

You did so well on the first problem. Six Flags decided to promote you to work on a more complicated ride. This new ride is a "Dog Chasing the Rabbit" ride. Passengers sit in the compartment labeled the "Dog." A mechanical "Rabbit" zooms by at a constant speed of 103 ft/sec. Three seconds later, starting from rest, the "Dog" starts accelerating at 10 ft/scc2 until it reaches a velocity of 125 ft/sec. The "Dog" then continues at a constant velocity of 125 ft/sec. What is the total time that it takes for the "Dog" to catch the "Rabbit?"?

Explanation / Answer

The time for the dog to reach 125 ft/s is

t1 = vdog/a =125/10 = 12.5 s

The total distance it travels is

S1 = s0 + v0 t + at^2/2 = 10*12.5^2/2 = 781.25 ft

The distance the rabbit travels

Srab = vrab(t1+3) = 103*(12.5+3) = 1596.5 ft

The distance between the dog and the rabbit at this moment is

Sd = 1596.5-781.25 = 815.25 ft

Let t be the additional time to catch the rabbit, then

vrab*t +815.25= vdog*t    =>   

103t+815.25 = 125t   = t = 37.06 s

Total time

ttotal = t1+t = 12.5+37.06 = 49.56 s

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