Kayla wishes to swim from one side of a river which has a cu

Kayla wishes to swim from one side of a river, which has a current speed of 2 km/h, to a point on the other side directly opposite from her starting point. She can swim at a speed of 3 km/h in still water.

a. At what angle to the bank should Kayla swim if she wishes to swim directly across?

b. If the river has a width of 300 m, how long will it take for her to cross the river?

c. If Kayla\'s speed and the river\'s speed had been reversed, explain why it would not have been possible for her to swim across the river?

Solution

Basically, Kayla needs to swim in a manner than allows for her swimming opposite of the current at 2 km/h. In other words, she needs to have a velocity vector breaks down into 2 two unit vector opposite the current and a total vector length of 3 units. So, vectors are like triangles. Kayla\'s triangle has a hypotenuse of 3 because that is the fastest she can go. A leg of the right triangle has to be 2 because that is the amount of her velocity she has to use to counter the current. It\'s direction is parallel to the the current. So since we have the adjacent and hypotenuse, we can use arccos to determine the angle. arcccos (2/3) = 48.19 degrees