# Answer to Question #26790 in Mechanics | Relativity for Corey

Question #26790

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?

Expert's answer

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

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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