How Do Currents Affect Swimming Across a River in Physics?

• roxxyroxx
In summary, a boy and a girl swim at 1.5 m/s and set out to cross a 50.0m wide river with a 1.0m/s southward current. The girl travels straight east and the boy is swept downstream while crossing. The velocity of the girl relative to the ground is 1.5 m/s, while the velocity of the boy relative to the ground is 2.29 m/s. They will be approximately 47.14m apart when they reach the opposite bank. Using the formula for finding the resultant of two vectors, we can calculate the angle and magnitude of the resultant velocity.
roxxyroxx

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?

The Attempt at a Solution

idk ?

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

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.

1. What are vectors in Physics 11?

A vector in Physics 11 is a quantity that has both magnitude and direction. It is represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

2. What is the difference between a scalar and a vector in Physics 11?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. For example, distance is a scalar quantity, while displacement is a vector quantity.

3. How do you add vectors in Physics 11?

To add vectors in Physics 11, you must first determine their components (magnitude and direction), then use the Pythagorean theorem to find the resultant magnitude, and finally use trigonometry to find the resultant direction.

4. Can vectors be negative in Physics 11?

Yes, vectors can have negative values in Physics 11. The direction of a vector can be positive or negative, depending on the coordinate system being used.

5. What are some real-life examples of vectors in Physics 11?

Some real-life examples of vectors in Physics 11 include velocity, acceleration, and force. These quantities have both magnitude and direction, making them vectors. For example, a car moving at 60 miles per hour in a north direction has a velocity of 60 mph and a displacement vector pointing north.

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