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A river 95.4 m wide flows toward the south at 32.2 m/min. A girl on the west bank wishes to reach the east bank in the least possible time. She can swim 95.4 m in still water in 1.55 min. What is the total distance she travels?

Answer :

Final answer:

The girl swims 95.4 m to cross the river, which is the distance she would travel in still water. In reality, she moves in a diagonal path due to the velocity of the river's current. More information is needed to calculate the total distance travelled relative to the shore.

Explanation:

The student wants to know the total distance the girl swims to cross the river. To understand this, we need to keep in mind that the girl's resultant speed combines two different movements: her speed swimming across the river, and the river's flow which displaces her downstream. Assuming she swims in a straight line right across the river, the distance she swims is the width of the river which is 95.4 m.

However, when considering the distance the girl travels relative to the river bank, she actually moves in a diagonal path. This path combines her speed through the water with the speed of the river, much like a boat trying to head straight across a river will actually move diagonally relative to the shore. This total velocity (solid arrow) relative to the shore is the sum of her velocity relative to the river plus the velocity of the river relative to the shore. To calculate this total distance, we will need more details such as the total time she spends in the water.

Learn more about velocity here:

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