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Relative Motion For a Child in a Stream

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A child in danger of drowning in a river is being carried downstream by a current that flows uniformly with a speed of 2.5 km/h. The child is 0.6 km from shore and 0.8 km upstream of a boat landing when a rescue boat sets out.

a) If the boat proceeds at its maximum speed of 20 km/h with respect to the water, what heading relative to the shore should the boatman take?

b) What angle does the boat velocity v make with the shore?

c) How long will it take the boat to reach the child?

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Solution Summary

229 words explain how to find the relative heading, boat velocity and length of time it will take for a boat to rescue a child drowning.

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(a)
Since the current flows uniformly, as soon as the boat is in the water it is carried downstream the same as the child.
Therefore in the frame of the water it does not matter that the shore is moving and the boat should take the heading in the direction of the child.

Let the direction upstream be the ...

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