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A boat has a water speed of 8.0m/s. The boat wishes to cross a river with a current of...

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boblee1245 | Student | eNoter

Posted February 22, 2012 at 10:08 AM via web

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A boat has a water speed of 8.0m/s. The boat wishes to cross a river with a current of 3.00m/s east.

If the boat points south for the entire trip, what will be the velocity of the boat relative to the shore and what direction should the boat point in order to cross the river to a point x, directly south across the river?

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najm1947 | Elementary School Teacher | Valedictorian

Posted February 22, 2012 at 11:31 AM (Answer #1)

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There are two parts to this question knowing the river flows due east with a velocity of 3.00m/s.

1. If the boat points due south what is its velocity relative to shore.

2. What should be its direction if has to reach a point "x" due south accross the river.

The velocity of boat is 8.00m/s.

The two parts are solved as under:

1. The magnitude of velocity relative to shore is the vector sum of two velocities and is equal to sqrt(8^2+3^2) = sqrt(73) = 8.54m/s

2. To hit the point due south, the boat has to move in the south-west direction in such a direction that the due west component of the boat velocity balances the east-wards velocity of the river flow. if 'a' angle of the baot with the shore, than 8.cos(a)=3

cos(a) = 3/8, a = 68 degrees

Thus:

1. The velocity of boat relative to shore is 8.54 m/s if boat moves due south

2. The boat should point South-West 68 degrees with shore to cross the river to reach point x directly south across the river.

This is possible

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