a dog is running at 9.5ms and is 40m behind a rabbit moving at 5.5ms. how long will it take the dog to catch the rabbit and how far did they travel?
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Expert's answer
2013-04-08T08:12:11-0400
a dog is running at 9.5ms and is 40m behind a rabbit moving at 5.5ms. how long will it take the dog to catch the rabbit and how far did they travel?
Vd = 9.5 m/s - velocity of dog Vr = 5.5 m/s - velocity of rabbit L0 = 40 m - initial distance between dog and rabbit
Suppose, dog's coordinate at initial moment equals 0. Therefore, dog's coordinate at time t: Sd = Vd*t, and for rabbit: Sr = L0 + Vr*t the dog will catch the rabbit when Sd = Sr: Vd*t = L0 + Vr*t Solving this equation: t = L0/(Vd - Vr) = 40m/(9.5 m/s - 5.5 m/s) = 10 s
Dog will travel distance: Ds = Vd*t = 9.5 m/s *10s = 95 m Rabbit will travel distance: Dr = Vr*t = 5.5 m/s *10s = 55 m
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