Question

An athlete in a competition needs to get from point A to another point B directly across from a river. He can swim in stationary water at a speed of 2.0 mi/h, and he can run at a speed of 5.0 mi/h. If the river does not flow, then to get from A to B he would certainly choose to swim directly across. But the river flows at a speed of 1.5 mi/h downstream. Given that, what would his strategy be in order to minimize the total time it takes to move from A to B? i.e., at what angle upstream (measured from the line AB) should he be swimming?

Answer 1

If the river is flowing downstream at 1.5 mi/h and he can swim 2.0 mi/h then the angle he would need to swim at in order to swim straight across would be arctan(1.5/2) which is equal to 36.87 degrees. This is because you can form a right triangle with 1.5 being opposite the angle and the 2.0 as the length adjacent to the angle. With regards to what his strategy should be, I don't know since you didn't provide what the land distance would be.

Answer 2

When you lift a bowling ball with a force of 86 N, the ball accelerates upward with an acceleration a. If you lift with a force of 96 N, the ball's acceleration is 2a.