# Motion in 2 Directions: An Algebraic Approach

• gungo
In summary, the conversation discusses a swimmer jumping into a river and swimming straight to the other side at a speed of 0.87 km/h [N]. It is mentioned that there is a current in the river of 2.0 km/h [W]. The two questions asked are: a) how long does it take the swimmer to reach the other side, and b) how far downstream has the current moved her by the time she reaches the other side. The equations used to solve these questions are v=d/t and a^2+b^2=c^2. The correct answer for Part A is found using the swimmer's speed of 0.87 km/h [N] and the distance of 5.
gungo

## Homework Statement

A swimmer jumps into a 5.1 km river and swims straight to the other side at 0.87 km/h [N].
There is a current in the river of 2.0 km/h [W]
a)How long does it take the swimmer to reach the other side?
b)How far downstream has the current moved her by the time she reaches the other side?

v= d/t
a^2+b^2=c^2

## The Attempt at a Solution

a) I got the correct answer but I don't understand why the 0.87 km/h [N] was used instead of the 2.0 km[W]
t=d/v
t=5.1/0.87
t=5.9 hrs
b) total velocity= √0.87^2+2^2
=2.18
I'm really not sure what I'm trying to look for??

Your answer to Part A was correct because motion in the X direction is independent of motion in the Y direction.
As the swimmer swims to the other side, you're given the swimmer's speed as she swims across. The current of the river doesn't affect the time it takes for the swimmer to reach the other side.

For Part B, you want how far she's been taken down stream during the time it took for her to reach the other side, or delta X.
Let me know if you have any other questions.

## 1. What is motion in 2 directions?

Motion in 2 directions, also known as two-dimensional motion, refers to the movement of objects in both the horizontal and vertical directions simultaneously.

## 2. What is the algebraic approach to studying motion in 2 directions?

The algebraic approach to studying motion in 2 directions involves using mathematical equations and formulas to analyze the motion of an object, rather than relying solely on visual representations or physical experiments.

## 3. How is velocity calculated in motion in 2 directions?

In motion in 2 directions, velocity is calculated by finding the displacement in both the horizontal and vertical directions and using the Pythagorean theorem to find the resultant displacement. The resultant displacement can then be divided by the total time to find the average velocity.

## 4. What is the difference between velocity and speed in motion in 2 directions?

Velocity and speed both refer to how fast an object is moving, but velocity also includes the direction of movement. Speed is a scalar quantity, while velocity is a vector quantity that includes both magnitude and direction.

## 5. How is acceleration calculated in motion in 2 directions?

In motion in 2 directions, acceleration is calculated by finding the change in velocity in both the horizontal and vertical directions and using the Pythagorean theorem to find the resultant change in velocity. The resultant change in velocity can then be divided by the total time to find the average acceleration.

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