Answer to Question #26790 in Mechanics | Relativity for Corey

Question

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?

Answer 1

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