Question

A member of a swim team is training by swimming in a river. The river is flowing uniformly at a constant speed of 2.20 m/s between parallel banks 84.0 m apart. The swimmer can only swim at a constant speed of 1.50 m/s. (a) Find the direction (in degrees), relative to the flow of the river, in which the swimmer must head to minimize the time spent in the water. (° from the direction of the stream) (b) How far (in m) downstream will the swimmer be carried? (c) The swimmer returns to the original starting point and decides to minimize the distance carried downstream. Find the new direction (in degrees) relative to the flow of the river. (° from the direction of the stream) (d) How far (in m) downstream will the swimmer be carried?

Answer 1

The swimmer should swim at 90 degrees to the river flow to minimize time in the water. To minimize distance downstream, the swimmer must calculate the angle considering velocity components, which requires additional data not provided in the question.

Step-by-step explanation:

The question pertains to a swimmer moving in river currents, a common problem in physics relating to relative velocity and vector addition. The situation involves calculating the optimal angles and positions for the swimmer to achieve certain objectives relative to the current flow.

Part (a)

To minimize the time spent in the water, the swimmer must swim directly across the river, or at 90 degrees to the flow, thus no calculation is required. At this angle, the river current does not affect the time taken to cross.

Part (b)

The swimmer is carried downstream by the river current while swimming across. To find the distance carried downstream, we would need to calculate the time taken to swim 84.0 m at 1.50 m/s and then multiply by the velocity of the river.

Part (c) and (d)

To minimize the distance downstream, we would need to calculate the swimming angle using vector components where the swimmer's swimming velocity components neutralize the flow velocity. The resultant path taken would be more challenging to compute without additional given data.