A dog searching for a bone walks 3.5 m south, then 8.20 m at an angle 30.0 north of east, and finally 15.0 m west. Using graphical techniques, find the dogs resultant displacement vector.
8.2 at NE = 5.8N and 5.8E
(0,-3.5)+(5.8,5.8)+(-15,0) = (-9.2,2.3)
(a) sqrt(9.2^2 + 2.3^2) = 9.48
(b) arctan(2.3/-9.2) = 166 deg
How come is the vector 8.2 defined into 5.8 N and 5.8 E ??. It's declared that the angle is 30° so it must be 7.1 E and 4.1 N.
To find the dog's resultant displacement vector, we need to add up the individual displacements the dog made in each direction:
1. Start by drawing a coordinate system with the origin as the starting point of the dog.
2. Draw an arrow representing the first displacement of 3.5 m south starting from the origin. Label this vector as "A".
3. From the end point of vector A, draw an arrow representing the second displacement of 8.20 m at an angle 30.0 north of east. Label this vector as "B".
4. To add vector B to vector A, draw vector B starting from the end point of vector A. This is done by drawing a line segment parallel to the x-axis for 8.20 m, and then drawing a line segment at an angle of 30.0 degrees north of east for the remaining distance. Label this resultant vector as "C".
5. From the end point of vector C, draw an arrow representing the third displacement of 15.0 m west. Label this vector as "D".
6. To find the resultant displacement vector, draw a line from the starting point (origin) to the end point of vector D. Label this vector as "R" for resultant displacement.
7. Measure the magnitude of vector R using a ruler. The magnitude represents the total distance traveled by the dog.
8. Measure the angle between vector R and the x-axis. This represents the direction of the resultant displacement vector.
Once you have completed these steps, you will have determined the dog's resultant displacement vector using graphical techniques.
To find the dog's resultant displacement vector, we can use graphical techniques. Here's how you can do it step by step:
1. Draw a reference frame: Start by drawing a horizontal x-axis (east/west direction) and a vertical y-axis (north/south direction) on a sheet of paper.
2. Start at the origin: Place a point at the origin (0, 0) on your reference frame. This represents the starting point of the dog's journey.
3. Draw the first displacement: From the starting point, draw an arrow representing the first displacement of 3.5 m south. To do this, go straight down from the starting point for a distance of 3.5 units on the y-axis.
4. Draw the second displacement: Next, draw an arrow representing the second displacement of 8.20 m at an angle 30.0 north of east. To do this, measure 8.20 units at a 30.0º angle from the east direction. This means you will move both horizontally and vertically. Use a protractor to measure the angle accurately.
5. Connect the dots: After drawing the first and second displacement arrows, connect the end point of the first displacement to the starting point of the second displacement with a straight line.
6. Draw the third displacement: From the end point of the second displacement, draw an arrow representing the third displacement of 15.0 m west. To do this, move horizontally to the left on the x-axis for a distance of 15.0 units.
7. Find the resultant displacement: The resultant displacement is the straight line connecting the starting point to the end point of the final displacement arrow. Measure the distance and direction (angle) of this line using a ruler and protractor, respectively.
8. Determine the magnitude and direction: Finally, calculate the magnitude of the resultant displacement by using the Pythagorean theorem. The magnitude is equal to the square root of the sum of the squares of the horizontal and vertical components of the resultant displacement. To find the direction of the resultant displacement, measure the angle it makes with the positive x-axis.
By following these steps, you should be able to determine the dog's resultant displacement vector using graphical techniques.