Leila walks South for 20m and then west for 20m. Determine her resultant displacement graphically and by calculation
45 degrees South of West
45 degrees West of South
x = -20
y = -20
hypotenuse = sqrt (400+400)
= 20 sqrt 2
remember 1, 1, sqrt 2
right isosceles triangle?
To determine Leila's resultant displacement both graphically and by calculation, we can use the principles of vector addition.
1. Graphical Method:
To determine the resultant displacement graphically, we can draw a scale diagram using a coordinate plane. Let's assume the starting point is the origin (0,0).
- Leila walks south for 20m, meaning she moves downward on the y-axis from the origin. We can draw an arrow pointing downwards, with a length representing 20 units.
- Leila then walks west for 20m, meaning she moves to the left on the x-axis. We can draw an arrow pointing leftwards, with a length representing 20 units.
- To find the resultant displacement, we draw a vector from the starting point (origin) to the endpoint of the last displacement. In this case, it will be a diagonal line connecting the starting point to the endpoint of the second displacement arrow.
- Measure the length of the resultant vector using a ruler or scale. This length represents the magnitude of the resultant displacement.
2. Calculation Method:
To calculate the resultant displacement, we can use the Pythagorean theorem and trigonometry.
- Since Leila walks 20m south and 20m west, we have a right-angled triangle.
- Using the Pythagorean theorem, the magnitude of the resultant displacement (R) can be calculated as:
R = sqrt((20^2) + (20^2)) = sqrt(400 + 400) = sqrt(800) ≈ 28.28m (rounded to two decimal places).
- To find the direction of the resultant displacement, we can use inverse trigonometric functions. In this case, we can use the tangent function:
tan(theta) = opposite/adjacent = 20/20 = 1
theta = tan^(-1)(1) ≈ 45 degrees
Therefore, the direction of the resultant displacement is 45 degrees west of south.
So, Leila's resultant displacement is approximately 28.28m at an angle of 45 degrees west of south.