Physics
Answers
The underlying idea in this problem is the concept of vector addition and resolution. Since the river is flowing at a constant speed in one direction said direction is known as the "x-direction" while the direction of your swim is the " y-direction." The river is flowing at a constant rate of 2.53 m/s in the x-direction. This is your vector vx. You are swimming at 1.74 m/s in the y-direction. This is your vector vy. To find the direction you need to swim, to minimize the time spent in the water, you need to solve for the angle θ using the equation: θ = tan-1 (vy/vx) The angle θ = tan-1 (1.74/2.53) = ~37.7° from the direction of the stream. To find the distance downstream carried, you can use the equation: Distance downstream = vx * time Where time is the time taken to cover the distance of 69.8 m across the river. To solve for time you can use the equation: time = s/v Where s is the distance across the river (69.8 m) and v is the combined velocity
