A girls walks 12m northwards 5m eastwards and 7m southwards her total displacement is?
Well, it sounds like this girl is on quite the adventure! To find her total displacement, we can imagine her journey using a Cartesian coordinate system. Moving northwards adds to her y-coordinate, moving eastwards adds to her x-coordinate, and moving southwards subtracts from her y-coordinate.
So, starting at the origin, she moves 12m northwards, which gives her a y-coordinate of +12. Then she moves 5m eastwards, adding to her x-coordinate, which becomes +5. Lastly, she moves 7m southwards, subtracting from her y-coordinate, which becomes +5 - 7 = -2.
Her final position is at coordinates (5, -2). To find her total displacement, we can use the Pythagorean theorem: displacement = √(x^2 + y^2). Plugging in her coordinates, we have displacement = √[(5^2) + (-2^2)] = √(25 + 4) = √29.
Therefore, her total displacement is approximately √29 meters, but don't worry, she'll find her way back with a little creativity and a good sense of direction!
To calculate the total displacement, we need to find the vector sum of the individual displacements.
Given:
Northward displacement = 12m
Eastward displacement = 5m
Southward displacement = 7m
Step 1: Convert the displacements into their vector forms.
Northward displacement = 12m northward -> (0, 12)
Eastward displacement = 5m eastward -> (5, 0)
Southward displacement = 7m southward -> (0, -7)
Step 2: Add the vector forms of the displacements.
(0, 12) + (5, 0) + (0, -7) = (0 + 5 + 0, 12 + 0 - 7) = (5, 5)
Step 3: Convert the vector form back to magnitude and direction.
Magnitude = sqrt(5^2 + 5^2) = sqrt(50) = 7.07m (rounded to two decimal places)
Direction = arctan (5/5) = 45° or northeast direction
Therefore, the total displacement is 7.07m at a 45° angle in the northeast direction.
To find the total displacement of the girl, we need to find the net result of her movements in different directions.
First, let's consider the northward and southward movements. These movements are along the same line, so we can subtract the value of the southward movement from the northward movement: 12m - 7m = 5m north.
Next, let's consider the eastward movement. Since the northward and southward movements are already accounted for, the eastward movement is perpendicular to these and doesn't affect the north-south direction. Therefore, we can simply add the value of the eastward movement: 5m east.
So, the total displacement of the girl is 5m north and 5m east.
North = 12-7 = 5
East = 5
sqrt(25+25) = 25 sqrt 2 m
(but I assume you really meant mi, miles not meters)
45 degrees east of north