A car is driven east for a distance of 49 km, then north for 35 km, and then in a direction 33° east of north for 27 km. Draw the vector diagram and determine the total displacement of the car from its starting point.
What is the magnitude and direction?
To solve this question, we need to draw a vector diagram and use vector addition to determine the total displacement of the car.
1. Draw a coordinate system with east as the positive x-axis and north as the positive y-axis. Place a dot to represent the starting point of the car.
2. From the starting point, draw a vector 49 km long in the east direction. This vector represents the car's initial displacement.
3. From the end point of the first vector, draw a vector 35 km long in the north direction. This vector represents the car's second displacement.
4. Now, from the end point of the second vector, draw a vector 27 km long that is 33° east of the north direction. To do this, extend a line from the second vector with a 33° angle using a protractor or any other tool. Measure 27 km along this line and draw the final vector.
5. The vector diagram should show three vectors connected head to tail, forming a triangle.
6. To determine the total displacement, draw a straight line from the starting point to the end point of the final vector. This straight line represents the total displacement of the car.
7. Measure the magnitude of the total displacement using a ruler.
8. To find the direction of the total displacement, measure the angle between the positive x-axis (east) and the line you drew in step 6. Use a protractor to measure the angle.
Now that we have the vector diagram, magnitude, and direction, we can determine the answers to the question.
The magnitude of the total displacement can be measured from the vector diagram using a ruler.
The direction of the total displacement can be determined by measuring the angle between the positive x-axis and the line connecting the starting point and end point using a protractor or any other angle-measuring tool.
I hope this helps you solve the problem and determine the magnitude and direction of the car's total displacement!
To determine the total displacement of the car from its starting point, we can draw a vector diagram to represent each leg of the journey.
Step 1: Draw the first vector representing the 49 km distance traveled east. Start at the origin (starting point) and draw a line segment of 49 units in the positive x-direction (east).
Step 2: Draw the second vector representing the 35 km distance traveled north. Start from the end point of the first vector and draw a line segment of 35 units in the positive y-direction (north).
Step 3: Draw the third vector representing the 27 km distance traveled in a direction 33° east of north. Start from the end point of the second vector and draw a line segment of 27 units in a direction 33° east of north.
Step 4: Draw the final vector to connect the origin (starting point) to the end point of the third vector. This vector represents the total displacement of the car.
Step 5: Measure the magnitude (length) and direction of the final vector using a ruler and a protractor. The magnitude of the vector can be found by measuring its length in the diagram. The direction of the vector can be found by measuring the angle it makes with the positive x-axis.
Step 6: Calculate the magnitude and direction of the vector using the measurements obtained.