A dog runs west for 20m then North for 15m. What is the resultant displacement of the dog graphically and by calculations
Displacement is (square root 15^2 + 20^2)
you have to add the angle for DISPLACEMENT.
the angle is arctan(15/20) W of N
To find the resultant displacement of the dog graphically, you can use vector diagrams. Here's how you can do it step-by-step:
1. Draw a coordinate system with the x-axis representing the east-west direction and the y-axis representing the north-south direction.
2. Start at the origin (0,0) and mark this point as the starting position of the dog.
3. Draw an arrow to the left (west) from the starting point for a distance of 20m. This represents the displacement in the west direction.
4. From the end of the first displacement, draw an arrow upwards (north) for a distance of 15m. This represents the displacement in the north direction.
5. Draw the two displacement vectors as arrows, one from the origin to the end of the west displacement, and one from the end of the west displacement to the end of the north displacement.
6. The resultant displacement is the straight line drawn from the starting point (origin) to the end of the last displacement vector.
To find the resultant displacement of the dog by calculations, you can use the Pythagorean theorem and trigonometry. Here's how you can do it step-by-step:
1. Use the Pythagorean theorem to find the magnitude of the resultant displacement. The magnitude is given by √(x² + y²), where x is the displacement in the x-direction (west) and y is the displacement in the y-direction (north).
Magnitude = √(20² + 15²) = √(400 + 225) = √625 = 25m
2. Use trigonometry to find the direction of the resultant displacement. The direction is given by the inverse tangent (arctan) of y/x.
Direction = arctan(15/20) = arctan(0.75) ≈ 36.9 degrees
Therefore, the resultant displacement of the dog is a magnitude of 25m in a direction of approximately 36.9 degrees north of west.