How Do Currents Affect Swimming Across a River in Physics?

[roxxyroxx]

Physics 11 vector help please?

Homework Statement

A boy and a girl both swim at 1.5 m/s. they set out together to cross a river that is 50.0m across and has a current flowing south at 1.0m/s.the girl takes a heading so she'll travel straight east across the river. meanwhile, the boy maintains an eastward heading that causes him to be swept downstream while crossing.
What is the velocity of the girl relative to the ground?
What is the velocity of the boy relative to the ground?
how far apart will they be when both have reached the opposite bank?

Homework Equations

The Attempt at a Solution

idk ?

 

[rl.bhat]

Since girl travels straight across the river, the resultant of two velocities ( girl's and river's) is perpendicular to the velocity of the river.
If R is the resultant of two vectors P and Q having an angle theta, then the angle between R and P is given by
tan(alpha) = Qsin(theta)/[P + Qcos(theta)]. In the above problem alpha = 90 degree. Find theta and R

 

[thomate1]

As a physicist, I would suggest breaking down the problem into its fundamental components and using vector addition to solve it. First, we need to define the coordinate system and establish the direction of the river's current as the negative y-axis. Then, we can use the given velocities of the boy and girl as vectors in the x-direction (east) and add them to the velocity of the river's current vector in the y-direction (south). This will give us the velocities of the boy and girl relative to the ground.

To find the distance between the boy and girl when they reach the opposite bank, we can use the distance formula and plug in the velocities we found earlier.

In summary, we need to use vector addition and the distance formula to solve this problem. If you need more help, I suggest consulting your textbook or asking your teacher for clarification on vector addition and how to apply it to this problem.