8. A dog with mass m is located at the far end with respect to the shore of a bo

Question

8. A dog with mass m is located at the far end with respect to the shore of a boat of mass M and length L. At this time, the dog is located a distance D from the shore as seen in the figure below. The dog starts moving toward the shore. (a) What is the relationship between the velocity of the dog relative to the ground and the velocity of the boat relative to the ground? (b) At what coordinate xp with respect to the shore will the dog be located when it will have moved a distance d with respect to the boat toward the shore? Express x, in terms of m, M and D and discuss what happens in the limit that the boat is much more massive than the dog. CMB

Explanation / Answer

let velocity of dog relative to ground = u (towards shore)

and velocity of boat relative to ground = -v (away from shore)

=> m(u - v) = (M + m)(-v)

=> mu = -Mv => u = -(M/m)v

b) when dog moves d wrt boat, boat moves distance y away from shore

md = (M+m)y => y = md/(M+m)

=> dog location , xD = D - d + y = D - d + (md/(M+m)) = D - (Md/(M+m))

if M >>m => xD = D - d

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