A car is driven 145 km west and then 65 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?
That did not work...
You must not have done the vector addition correctly. If you show your work, the error can probably be found.
You will need to use the Pythagorean relation for the magnitude.
The sin and cos of 45 degrees are both 0.707
A car is driven 115 km west and then 85 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?
a car travels 80 km due north and then 140 km in the direction west of north. find the magnitude and direction of the cars resultant displacementby drawing an accurate scale diagram.
To find the displacement of the car from the point of origin, we need to calculate the net distance and direction from the starting point.
First, let's break down the car's movements into horizontal and vertical components. The initial movement of 145 km west is a horizontal distance, so it only affects the x-coordinate. The second movement of 65 km southwest affects both the x and y-coordinates.
Next, we'll calculate the horizontal and vertical distances separately.
For the horizontal distance:
The car is driven 145 km west, which means the x-coordinate decreases by 145 km.
For the vertical distance:
The car is driven 65 km southwest. To calculate the vertical distance, we need to determine the horizontal and vertical components of this movement.
The southwest direction can be divided into two perpendicular directions: south (vertical component) and west (horizontal component). A southwest direction forms a 45-degree angle with each of these axes.
To calculate the components:
Vertical component = 65 km * sin(45 degrees)
Horizontal component = 65 km * cos(45 degrees)
You can use a calculator or trigonometric identities to find the sine and cosine values.
Now that we have all the components, we can find the net displacement.
Net horizontal displacement = -145 km + horizontal component of southwest movement
Net vertical displacement = vertical component of southwest movement
To find the magnitude (total displacement), we'll use the Pythagorean theorem:
Displacement (magnitude) = √((Net horizontal displacement)^2 + (Net vertical displacement)^2)
Finally, to find the direction of the displacement, we'll use inverse trigonometry:
Direction = atan2(Net vertical displacement, Net horizontal displacement)
Using these calculations, you can find the magnitude and direction of the car's displacement from the point of origin.
Add the two vectors.
Net displacement west is 145 + 65 cos45
Net displacement south is 65 sin45