What Speed Should a Swimmer Have to Cross a River Directly?

[frangieh]

Homework Statement

A swimmer wants to cross a river, from point A to point B, as shown in the figure. The distance d_1 (from A to C) is 200 m, the distance d_2 (from C to B) is 150 m and the speed v_r of the current in the river is 5 {km/hour}. Suppose that the swimmer's velocity relative to the water makes an angle of \theta = 45\;{degrees} with the line from A to C, as indicated in the figure.


To swim directly from A to B, what speed u_s, relative to the water, should the swimmer have?

 

[Andrew Mason]

Homework Statement

A swimmer wants to cross a river, from point A to point B, as shown in the figure. The distance d_1 (from A to C) is 200 m, the distance d_2 (from C to B) is 150 m and the speed v_r of the current in the river is 5 {km/hour}. Suppose that the swimmer's velocity relative to the water makes an angle of \theta = 45\;{degrees} with the line from A to C, as indicated in the figure.


To swim directly from A to B, what speed u_s, relative to the water, should the swimmer have?

Homework Statement

This is a vector problem. Do a vector diagram showing the velocity vector for the swimmer relative to water and the velocity vector for the water relative to land. How is the velocity vector of the swimmer relative to land related to these two vectors?

AM

 

[frangieh]

A swimmer wants to cross a river, from point A to point B, as shown in the figure. The distance d_1 (from A to C) is 200 m, the distance d_2 (from C to B) is 150 m, and the speed v_r of the current in the river is 5 {km/hour}. Suppose that the swimmer's velocity relative to the water makes an angle of \theta = 45 degrees} with the line from A to C,

o swim directly from A to B, what speed u_s, relative to the water, should the swimmer have?

Vs =4.04 km/hour

because Vs =D1*vr(d1*sin(theta)+ d2*cos(theta))