# Two-Dimensional Motion and Vectors

• eaglesfan94
In summary, the total displacement when driving along this part of U.S. Highway 212 would be 115km. This is calculated using the given distances and directions using the formula d^2=X^2+Y^2.
eaglesfan94

## Homework Statement

U.S. Highway 212 extends 55km at 37 degrees north of east between Newell and Mud Butte, south Dakota. It then continues for 66 km nearly due east from Mud Butte to Faith, South Dakota. If you drive alongthis part of U.S. Highway 212, what will your total displacement be?

X1=55(cos37) Y1=55(sin37)
X2=66(cos0) Y2=66(sin0)

d^2=X^2+Y^2

## The Attempt at a Solution

D=115km

eaglesfan94 said:

## Homework Statement

U.S. Highway 212 extends 55km at 37 degrees north of east between Newell and Mud Butte, south Dakota. It then continues for 66 km nearly due east from Mud Butte to Faith, South Dakota. If you drive alongthis part of U.S. Highway 212, what will your total displacement be?

X1=55(cos37) Y1=55(sin37)
X2=66(cos0) Y2=66(sin0)

d^2=X^2+Y^2

D=115km

## 1. What is two-dimensional motion?

Two-dimensional motion refers to the movement of an object in two perpendicular directions, typically represented by the x and y axes. This type of motion can be described using vectors, which include both magnitude (distance or speed) and direction.

## 2. What are vectors?

Vectors are mathematical quantities that have both magnitude (size) and direction. They are often used to represent physical quantities such as displacement, velocity, and force in two-dimensional motion. Vectors can be added, subtracted, and multiplied to describe the overall motion of an object.

## 3. How is displacement different from distance?

Displacement is a vector quantity that describes the change in position of an object from its starting point to its ending point. It takes into account both the magnitude and direction of the movement. Distance, on the other hand, is a scalar quantity that only describes the total length of the path traveled by the object, regardless of direction.

## 4. What is the difference between speed and velocity?

Speed is a scalar quantity that describes how fast an object is moving, regardless of direction. It is measured in units of distance per unit of time (e.g. meters per second). Velocity, on the other hand, is a vector quantity that describes how fast an object is moving in a specific direction. It is measured in units of distance per unit of time with a specified direction (e.g. 10 meters per second south).

## 5. How are vectors represented graphically?

Vectors can be represented graphically using arrows. The length of the arrow represents the magnitude of the vector, while the direction of the arrow represents the direction of the vector. The starting point of the arrow can also indicate the initial position of the object, while the ending point represents the final position after the movement described by the vector.